Prove the following: (cos 9x - cos 5x) / (sin 17x - sin 3x) = -sin 2x / cos 10x

Solution:

LHS = (cos 9x - cos 5x) / (sin 17x - sin 3x)

Using trigonometric formula,

Since cos A - cos B = -2sin [(A + B) / 2] sin [(A - B) / 2] and sin A - sin B = 2cos [(A + B) / 2] sin [(A - B) / 2],

= [-2sin (9x + 5x)/2 sin (9x - 5x)/2] / [2cos (17x + 3x)/2 sin (17x - 3x)/2]     

= [-2sin 7x sin 2x] / [2cos 10x sin 7x]

= -sin 2x / cos 10x 

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 16

Prove the following: (cos 9x - cos 5x) / (sin 17x - sin 3x) = -sin 2x / cos 10x

Summary:

We got, (cos 9x - cos 5x) / (sin 17x - sin 3x) = -sin 2x / cos 10x. Hence Proved