Prove that cos π 3 + x = 1 2 ( cos x - 3 sin x ) .

To prove that cos π 3 + x = 1 2 ( cos x - 3 sin x ) . We know that cos A + B = cos A cos B - sin A sin B . Now, cos π 3 + x = cos π 3 cos x - sin π 3 sin x = 1 2 · cos x - 3 2 · sin x = 1 2 ( cos x - 3 sin x ) Hence, proved.

Prove that sin π 4 + x + sin π 4 - x = 2 cos x .

To prove that sin π 4 + x + sin π 4 - x = 2 cos x Now, sin π 4 + x + sin π 4 - x = sin π 4 cos x + cos π 4 sin x + sin π 4 cos x - cos π 4 sin x = 1 2 cos x + 1 2 sin x + 1 2 cos x - 1 2 sin x = 2 2 cos x = 2 cos x Hence, proved.

Prove that 1 2 cos π 4 + x = 1 2 ( cos x - sin x ) .

To prove that 1 2 cos π 4 + x = 1 2 ( cos x - sin x ) . Now, 1 2 cos π 4 + x = 1 2 cos π 4 cos x - sin π 4 sin x ∵ cos A + B = cos A cos B - sin A sin B = 1 2 1 2 cos x - 1 2 sin x = 1 2 ( cos x - sin x ) Hence, proved.

Prove that cos x + cos 2 π 3 + x + cos 2 π 3 - x = 0 .

To prove that cos x + cos 2 π 3 + x + cos 2 π 3 - x = 0 . Now, cos x + cos 2 π 3 + x + cos 2 π 3 - x = cos x + cos 2 π 3 cos x - sin 2 π 3 sin x + cos 2 π 3 cos x + sin 2 π 3 sin x = cos x + 2 cos 2 π 3 cos x = cos x + 2 cos π - π 3 cos x = cos x - 2 cos π 3 cos x ∵ cos π - θ = - cos θ = cos x - 2 1 2 cos x = cos x - cos x = 0 Hence, proved.

Prove that 2 sin 5 π 12 sin π 12 = 1 2 .

To prove that 2 sin 5 π 12 sin π 12 = 1 2 . Now, 2 sin 5 π 12 sin π 12 = cos 5 π 12 - π 12 - cos 5 π 12 + π 12 ∵ 2 sin A sin B = cos A - B - cos A + B = cos 4 π 12 - cos 6 π 12 = cos π 3 - cos π 2 = 1 2 - 0 = 1 2 Hence, proved.

Prove that 2 cos 5 π 12 cos π 12 = 1 2 .

To prove that 2 cos 5 π 12 cos π 12 = 1 2 . Now, 2 cos 5 π 12 cos π 12 = cos 5 π 12 + π 12 + cos 5 π 12 - π 12 ∵ 2 cos A cos B = cos A + B + cos A - B = cos 6 π 12 + cos 4 π 12 = cos π 2 + cos π 3 = 0 + 1 2 = 1 2 Hence, proved.

Prove that 2 sin 5 π 12 cos π 12 = ( 2 + 3 ) 2 .

To prove that 2 sin 5 π 12 cos π 12 = ( 2 + 3 ) 2 . Now, 2 sin 5 π 12 cos π 12 = sin 5 π 12 + π 12 + sin 5 π 12 - π 12 ∵ 2 sin A cos B = sin A + B + sin A - B = sin 6 π 12 + sin 4 π 12 = sin π 2 + sin π 3 = 1 + 3 2 = ( 2 + 3 ) 2 Hence, proved that 2 sin 5 π 12 cos π 12 = ( 2 + 3 ) 2 .

E M B I B E

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

R S Aggarwal Solutions for Exercise 2: EXERCISE 2B

Author:R S Aggarwal

R S Aggarwal Mathematics Solutions for Exercise - R S Aggarwal Solutions for Exercise 2: EXERCISE 2B

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

Questions from R S Aggarwal Solutions for Exercise 2: EXERCISE 2B with Hints & Solutions

MEDIUM

11th West Bengal Board

IMPORTANT

WBCHSE Mathematics for Class 11>Chapter 11 - Trigonometric, or Circular, Functions>EXERCISE 2B>Q 18

If $\cos x = \frac{3}{5}$ and $\cos y = \frac{- 24}{25}$ , where $\frac{3 π}{2} < x < 2 π$ and $π < y < \frac{3 π}{2}$ , find the value of $\tan (x + y)$ .