Prove that 2 sin 22 1 2 ° cos 22 1 2 ° = 1 2 .

To prove that 2 sin 22 1 2 ° cos 22 1 2 ° = 1 2 Now, 2 sin 22 1 2 ° cos 22 1 2 ° = sin 2 22 1 2 ° ∵ 2 sin x cos x = sin 2 x = sin 45 ° = 1 2 Hence, proved.

Prove that 2 cos 2 15 ° - 1 = 3 2 .

To prove that 2 cos 2 15 ° - 1 = 3 2 . Now, 2 cos 2 15 ° - 1 = cos 2 15 ° ∵ cos 2 θ = 2 cos 2 θ - 1 = cos 30 ° = 3 2 Hence, proved.

Prove that 3 sin 40 ° - 4 sin 3 40 ° = 3 2 .

To prove that 3 sin 40 ° - 4 sin 3 40 ° = 3 2 . Now, 3 sin 40 ° - 4 sin 3 40 ° = sin 3 40 ° ∵ sin 3 x = 3 sin x - 4 sin 3 x = sin 120 ° = sin 180 ° - 60 ° = sin 60 ° ∵ sin ( π - θ ) = sin θ = 3 2 Hence, proved.

Prove that sin 2 24 ° - sin 2 6 ° = 5 - 1 8 .

To prove, sin 2 24 ° - sin 2 6 ° = 5 - 1 8 Now, sin 2 24 ° - sin 2 6 ° = sin 24 ° + 6 ° sin 24 ° - 6 ° ∵ sin 2 x - sin 2 y = sin ( x - y ) sin ( x + y ) = sin 30 ° sin 18 ° = 1 2 · 5 - 1 4 = 5 - 1 8 Hence, proved.

Prove that sin 2 72 ° - cos 2 30 ° = 5 - 1 8 .

To prove sin 2 72 ° - cos 2 30 ° = 5 - 1 8 Now, sin 2 72 ° - cos 2 30 ° = cos 2 18 ° - 3 2 2 ∵ sin 72 ° = sin 90 ° - 18 ° = cos 18 ° = 1 - sin 2 18 ° - 3 4 ∵ sin 2 x + cos 2 x = 1 = 1 4 - 5 - 1 4 2 = 4 16 - ( 5 + 1 - 2 5 ) 16 = - 2 + 2 5 16 = 5 - 1 8 Hence, proved.

If tan θ = a b prove that a sin 2 θ + b cos 2 θ = b .

Given, tan θ = a b To prove that a sin 2 θ + b cos 2 θ = b . Now, a sin 2 θ + b cos 2 θ = a 2 tan θ 1 + tan 2 θ + b 1 - tan 2 θ 1 + tan 2 θ = a 2 a b 1 + a b 2 + b 1 - a b 2 1 + a b 2 = a 2 a b b 2 + a 2 b 2 + b b 2 - a 2 b 2 b 2 + a 2 b 2 = 2 a 2 b b 2 + a 2 + b b 2 - a 2 b 2 + a 2 = 2 a 2 b + b b 2 - a 2 b b 2 + a 2 = a 2 b + b b 2 b 2 + a 2 = b a 2 + b 2 b 2 + a 2 = b Hence, proved.

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WBCHSE Mathematics for Class 11>Trigonometry>Chapter 11 - Trigonometric, or Circular, Functions>EXERCISE 2D

R S Aggarwal Solutions for Exercise 4: EXERCISE 2D

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Exercise 4: EXERCISE 2D

Attempt the practice questions from Exercise 4: EXERCISE 2D with hints and solutions to strengthen your understanding. WBCHSE Mathematics for Class 11 solutions are prepared by Experienced Embibe Experts.