Chapter 5 Trigonometric Functions Exercise Ex. 5.1

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Question 6

Solution 6

Question 7

Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

Question 13

Solution 13

Question 14

Solution 14

Question 15

Solution 15

Question 16

Prove that cosθ(tanθ+2)(2 tanθ+1)=2 secθ+5 sinθSolution 16

Question 17

I f space x equals fraction numerator 2 space sin space theta over denominator 1 plus cos space plus sin space theta end fraction comma space t h e n space p r o v e space t h a t space fraction numerator 1 minus cos space plus sin space theta over denominator 1 plus sin space theta end fraction i s space a l s o space e q u a l space t o space x.

Solution 17

fraction numerator 2 space sin space theta over denominator 1 plus cos space theta plus sin space theta end fraction equals x
rightwards double arrow fraction numerator 2 space sin space theta left parenthesis 1 minus cos space theta plus sin space theta right parenthesis over denominator left parenthesis 1 plus cos space theta plus sin space theta right parenthesis left parenthesis 1 minus cos space theta plus sin space theta right parenthesis end fraction equals x space space space left square bracket R a t i o n a l i z i n g space t h e space d e n o m i n a t o r right square bracket
rightwards double arrow fraction numerator 2 space sin space theta left parenthesis 1 minus cos space theta plus sin space theta right parenthesis over denominator left parenthesis 1 plus sin space theta right parenthesis squared minus cos squared space theta end fraction equals x
rightwards double arrow fraction numerator 2 space sin space theta minus 2 space sin space theta cos space theta plus 2 space sin squared theta over denominator 1 plus sin squared space theta plus 2 sin space theta minus cos squared space theta end fraction equals x
rightwards double arrow fraction numerator 2 space sin space theta left parenthesis 1 plus cos space theta minus sin space theta right parenthesis over denominator 2 sin squared space theta plus 2 space sin space theta end fraction equals x
rightwards double arrow fraction numerator 2 space sin space theta left parenthesis 1 plus cos space theta minus sin space theta right parenthesis over denominator 2 sin space theta left parenthesis 1 plus sin space theta right parenthesis end fraction equals x
rightwards double arrow fraction numerator 1 plus cos space theta space minus sin space theta over denominator 1 plus sin space theta end fraction equals x space left square bracket C a n c e l l i n g space t h e space 2 space sin space theta space i n space b o t h space N u m e r a t o r space a n d space D e n o m i n a t o r right square bracket
H e n c e space P r o v e d

Question 18

Solution 18

Question 19

I f space tan space theta equals a over b comma space t h e n space f i n d space t h e space v a l u e space o f space square root of fraction numerator a plus b over denominator a minus b end fraction end root plus square root of fraction numerator a minus b over denominator a plus b end fraction end root.

Solution 19

square root of fraction numerator a plus b over denominator a minus b end fraction end root plus square root of fraction numerator a minus b over denominator a plus b end fraction end root
equals square root of fraction numerator begin display style a over b end style plus 1 over denominator begin display style a over b end style minus 1 end fraction end root plus square root of fraction numerator begin display style a over b end style minus 1 over denominator begin display style a over b end style plus 1 end fraction end root space left square bracket D i v i d i n g space b o t h space N u m e r a t o r space a n d space d e n o m i n a t o r space b y space b right square bracket
equals square root of fraction numerator tan space theta plus 1 over denominator tan space theta minus 1 end fraction end root plus square root of fraction numerator tan space theta minus 1 over denominator tan space theta plus 1 end fraction end root
equals square root of fraction numerator begin display style fraction numerator sin space theta over denominator cos space theta end fraction end style plus 1 over denominator begin display style fraction numerator sin space theta over denominator cos space theta end fraction end style minus 1 end fraction end root plus square root of fraction numerator begin display style fraction numerator sin space theta over denominator cos space theta end fraction end style minus 1 over denominator begin display style fraction numerator sin space theta over denominator cos space theta end fraction end style plus 1 end fraction end root
equals square root of fraction numerator begin display style fraction numerator sin space theta plus cos space theta over denominator cos space theta end fraction end style over denominator begin display style fraction numerator sin space theta minus cos space theta over denominator cos space theta end fraction end style end fraction end root plus square root of fraction numerator begin display style fraction numerator sin space theta minus cos space theta over denominator cos space theta end fraction end style over denominator begin display style fraction numerator sin space theta plus cos space theta over denominator cos space theta end fraction end style end fraction end root
equals square root of fraction numerator sin space theta plus cos space theta over denominator sin space theta minus cos space theta end fraction end root plus square root of fraction numerator sin space theta minus cos space theta over denominator sin space theta plus cos space theta end fraction end root
equals fraction numerator sin space theta plus cos space theta plus sin space theta minus cos space theta over denominator square root of sin squared space theta minus cos squared space theta end root end fraction
equals fraction numerator 2 space sin space theta space over denominator square root of sin squared space theta space minus space cos squared space theta end root end fraction

Question 20

Solution 20

Question 21

Solution 21

Question 22

Solution 22

Question 23

Solution 23

Question 24

Syntax error from line 1 column 702 to line 1 column 707. Unexpected '</mi>'.

Solution 24

L H S space equals space a b plus a minus b plus 1
equals left parenthesis s e c space theta minus tan space theta right parenthesis left parenthesis cos e c space plus c o t space right parenthesis plus s e c space theta minus tan space theta minus cos e c space theta minus c o t space theta plus 1
equals open parentheses fraction numerator 1 over denominator cos space theta end fraction minus fraction numerator sin space theta over denominator cos space theta end fraction close parentheses open parentheses fraction numerator 1 over denominator sin space theta end fraction plus fraction numerator cos space theta over denominator sin space theta end fraction close parentheses plus fraction numerator 1 over denominator cos space theta end fraction minus fraction numerator sin space theta over denominator cos space theta end fraction minus fraction numerator 1 over denominator sin space theta end fraction minus fraction numerator cos space theta over denominator sin space theta end fraction plus 1
equals fraction numerator 1 over denominator sin space theta space cos space theta end fraction plus fraction numerator 1 over denominator cos space theta end fraction cross times fraction numerator cos space theta over denominator sin space theta end fraction minus fraction numerator sin space theta over denominator cos space theta end fraction cross times fraction numerator 1 over denominator sin space theta end fraction minus tan space theta cross times c o t space theta plus fraction numerator 1 over denominator cos space theta end fraction minus fraction numerator sin space theta over denominator cos space theta end fraction minus fraction numerator 1 over denominator sin space theta end fraction minus fraction numerator cos space theta over denominator sin space theta end fraction plus 1
equals fraction numerator 1 over denominator sin space theta space cos space theta end fraction plus fraction numerator 1 over denominator sin space theta end fraction minus fraction numerator 1 over denominator cos space theta end fraction minus 1 plus fraction numerator 1 over denominator cos space theta end fraction minus fraction numerator sin space theta over denominator cos space theta end fraction minus fraction numerator 1 over denominator sin space theta end fraction minus fraction numerator cos space theta over denominator sin space theta end fraction plus 1
equals fraction numerator 1 over denominator sin space theta space cos space theta end fraction minus fraction numerator sin space theta over denominator cos space theta end fraction minus fraction numerator cos space theta over denominator sin space theta end fraction
equals fraction numerator 1 over denominator sin space theta space cos space theta end fraction minus fraction numerator sin space theta over denominator cos space theta end fraction minus fraction numerator cos space theta over denominator sin space theta end fraction
equals fraction numerator 1 minus sin squared space theta minus cos squared space theta over denominator sin space theta. cos space theta end fraction
equals fraction numerator 1 minus left parenthesis cos squared space theta plus sin squared space theta right parenthesis over denominator sin space theta. space cos space theta end fraction
equals fraction numerator 1 minus 1 over denominator sin space theta. cos space theta end fraction equals 0 equals R H S. space H e n c e space P r o v e d

Question 25

Solution 25

Question 26(i)

Solution 26(i)

Question 26(ii)

Solution 26(ii)

Question 26(iii)

Solution 26(iii)

Chapter 5 Trigonometric Functions Exercise Ex. 5.2

Question 1(i)

Solution 1(i)

Question 1(ii)

Solution 1(ii)

Question 1(iii)

Solution 1(iii)

Question 1(iv)

Solution 1(iv)

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 5

Solution 5

Chapter 5 Trigonometric Functions Exercise Ex. 5.3

Question 1(i)

Solution 1(i)

Question 1(ii)

Solution 1(ii)

Question 1(iii)

Solution 1(iii)

Question 1(iv)

Solution 1(iv)

Question 1(v)

Solution 1(v)

Question 1(vi)

Solution 1(vi)

Question 1(vii)

Solution 1(vii)

Question 1(viii)

Solution 1(viii)

Question 1(ix)

Solution 1(ix)

Question 1(x)

Solution 1(x)

Question 1(xi)

Solution 1(xi)

Question 1(xii)

Solution 1(xii)

Question 1(xiii)

Solution 1(xiii)

Question 1(xiv)

Solution 1(xiv)

Question 2(i)

Solution 2(i)

Question 2(ii)

Solution 2(ii)

Question 2(iii)

Solution 2(iii)

Question 2(iv)

Solution 2(iv)

Question 2(v)

Solution 2(v)

Question 2(vi)

Solution 2(vi)

Question 2(vii)

Solution 2(vii)

Question 3(i)

Solution 3(i)

Question 3(ii)

Solution 3(ii)

Question 3(iii)

Solution 3(iii)

Question 3(iv)

Solution 3(iv)

Question 3(v)

Solution 3(v)

Question 4

Solution 4

Question 5

Solution 5

Question 6(i)

Solution 6(i)

Question 6(ii)

Solution 6(ii)

Question 6(iii)

Solution 6(iii)

Question 7

Solution 7

Question 8(i)

Solution 8(i)

Question 8(ii)

Solution 8(ii)

Question 9(i)

Solution 9(i)

Question 9(ii)

Solution 9(ii)

Question 9(iii)

Solution 9(iii)

Question 9(iv)

Solution 9(iv)

Question 9(v)

Solution 9(v)


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