Table of Contents
Exercise Ex. 7
Question 1
Without using trigonometric tables, evaluate:
Solution 1
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Question 2
Without using trigonometric tables, prove that:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)Solution 2
(i) LHS = cos81° – sin9°
= cos(90° -9°)- sin9° = sin9° – sin9°
= 0 = RHS
(ii) LHS = tan71° – cot19°
=tan(90° – 19°) – cot19° =cot19° – cot19°
=0 = RHS
(iii) LHS = cosec80° – sec10°
= cosec(90° – 10°) – sec(10°)
= sec10° – sec10° = 0
= RHS
(iv) LHS=
(v)
(vi)
(vii)
LHS = RHS
(viii)
(ix) LHS = (sin65° + cos25°) (sin65° – cos25°)
Question 3(i)
Without using trigonometric tables, prove that:
sin 53ᵒ cos37ᵒ + cos53ᵒ sin37ᵒ = 1Solution 3(i)
Question 3(ii)
cos 54ᵒ cos 36ᵒ – sin 54ᵒ sin36ᵒ = 0Solution 3(ii)
Question 3(iii)
sec 70ᵒ sin 20ᵒ + cos 20ᵒ cosec 70ᵒ = 2Solution 3(iii)
Question 3(iv)
sin 35ᵒ sin 55ᵒ – cos 35ᵒ cos 55ᵒ = 0Solution 3(iv)
Question 3(v)
(sin 72ᵒ + cos 18ᵒ)(sin72ᵒ – cos18ᵒ) = 0Solution 3(v)
Question 3(vi)
tan 48ᵒ tan 23ᵒ tan 42ᵒ tan 67ᵒ = 1Solution 3(vi)
Question 4(i)
Prove that:
Solution 4(i)
Question 4(ii)
Solution 4(ii)
Question 4(iii)
Solution 4(iii)
Question 4(iv)
Solution 4(iv)
Question 4(v)
Solution 4(v)
Question 5(i)
Prove that:
sin θ cos (90ᵒ – θ) + sin (90ᵒ – θ) cos θ = 1Solution 5(i)
Question 5(ii)
Solution 5(ii)
Question 5(iii)
Solution 5(iii)
Question 5(iv)
Solution 5(iv)
Question 5(v)
Solution 5(v)
Question 5(vi)
Solution 5(vi)
Question 5(vii)
Solution 5(vii)
Question 6(i)
Solution 6(i)
Question 6(ii)
Solution 6(ii)
Question 6(iii)
Solution 6(iii)
Question 6(iv)
cos 1ᵒ cos2ᵒ cos3ᵒ … cos 180ᵒ= 0Solution 6(iv)
Question 6(v)
Solution 6(v)
Question 7
Prove that:
(i)
(ii)
(iii)
(iv)
(v)Solution 7
(i) LHS =
= RHS
(ii) LHS =
= RHS
(iii) LHS =
= RHS
(iv) LHS = cosec(65° + ) – sec(25°- ) – tan(55° – ) + cot(35° + )
= RHS
(v) LHS =
= 0 + 1 = 1
= RHS
Question 8(i)
Express each of the following in terms of T-ratios of angles lying between 0ᵒ and 45ᵒ:
sin 67ᵒ + cos 75ᵒSolution 8(i)
Question 8(ii)
cot 65ᵒ + tan 49ᵒSolution 8(ii)
Question 8(iii)
sec 78ᵒ + cosec 56ᵒSolution 8(iii)
Question 8(iv)
cosec 54ᵒ + sin 72ᵒSolution 8(iv)
Question 9
If A, B, C are the angles of a triangle ABC, prove that:Solution 9
A + B + C = 180°
So, B + C= 180° – A
Question 10
If cos 2θ = sin 4θ, where 2θ and 4θ are acute angles, find the value of θ.Solution 10
Question 11
If sec 2A= cosec (A – 42ᵒ), where 2A is an acute angle, find the value of A.Solution 11
Question 12
If sin3A = cos(A – 26o), where 3A is an acute angle, find the value of A.Solution 12
Question 13
If tan 2A = cot(A – 12o), where 2A is an acute angle, find the value of A.Solution 13
Question 14
If sec 4A = cosec(A – 15o), where 4A is an acute angle, find the value of A.Solution 14
Question 15
Prove that:
Solution 15
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