Prove the following: (sin 5x + sin 3x) / (cos 5x + cos 3x) = tan 4x

Solution:

LHS = (sin 5x + sin 3x) / (cos 5x + cos 3x)

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

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

= sin 4x / cos 4x

= tan 4x

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 17

Prove the following: (sin 5x + sin 3x) / (cos 5x + cos 3x) = tan 4x

Summary:

We got, (sin 5x + sin 3x) / (cos 5x + cos 3x) = tan 4x, Hence Proved.