RD SHARMA SOLUTION CHAPTER-10 Sine and Cosine Formulae and Their Applications I CLASS 11TH MATHEMATICS-EDUGROWN

Chapter 10 Sine and Cosine Formulae and Their Applications Exercise Ex. 10.1

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

In any triangle ABC, prove the following:

b sinB – c sinC = a sin (B – C)Solution 11

Question 12

In any triangle ABC, prove the following:

a²sin(B – C)= (b² –c²)sinASolution 12

Question 13

Solution 13

Question 14

In any triangle ABC, prove the following:

a(sinB – sinC) + b (sinC – sinA) + c (sinA – sinB) = 0Solution 14

Question 15

Solution 15

Question 16

In any triangle ABC, prove the following:

a²(cos²B – cos²C) + b²(cos²C – cos²A) + c²(cos²A –cos²B) = 0Solution 16

Question 17

In any triangle ABC, prove the following:

b cosB + c cosC = a cos(B – C)Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 20

Solution 20

Question 21

Solution 21

Question 22

In any triangle ABC, prove the following:

a cosA + b cosB + c cosC= 2b sinA sinC= 2c sinA sinBSolution 22

Question 23

a(cos B cosC + cosA)= b(cos C cosA + cosB)= c(cos A cosB + cosC)Solution 23

Question 24

Solution 24

Question 25

In ΔABC prove that, if Ө be any angle, then b cosӨ = c cos(A – Ө) + a cos(C + Ө)Solution 25

Question 26

In a ΔABC, if sin²A + sin²B = sin²C, show that the triangle is right angled.Solution 26

Question 27

In any ΔABC, if a², b², c² are in A.P., prove that cot A, cot B and cot C are also in A.P.Solution 27

Question 28

The upper part of a broken over by the wind makes an angle of 30⁰ with the ground and the distance from the root to the point where the top of the tree touches the ground is 15m. Using sine rule, find the height of the tree.Solution 28

Question 29

At the foot of a mountain the elevation of its summit is 45⁰; after ascending 1000m towards the mountain up a slope of 30⁰ inclination, the elevation is found to be 60⁰. Find the height of the mountain.Solution 29

Question 30

Solution 30

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Question 31

Solution 31

Chapter 10 Sine and Cosine Formulae and Their Applications Exercise Ex. 10.2

Question 1

Solution 1

Question 2

Solution 2

Question 3

Solution 3

Question 4

Solution 4

Question 6

C (a cos B – b cos A) = a² – b²Solution 6

Question 7

2(bc cos A + ca cos B +ab cosC)= a² + b² + c²Solution 7

Question 8

Solution 8

Question 9

Solution 9

Question 10

Solution 10

Question 12

Solution 12

Question 13

Solution 13

Question 14

In a Δ ABC, prove that

sin³ A cos (B -C) + sin³B cos(C – A)+ sin³ C cos(A- B) = 3 sin A sin B sin CSolution 14

Question 15

Solution 15

Question 16

Solution 16

Question 17

Solution 17

Question 18

Solution 18

Question 19

Solution 19

Question 5

b(c cos A – a cos C) = c² –a²Solution 5

Question 11

In any DABC, prove the following:

a cos A + b cos B + c cosC = 2b sin A sin CSolution 11