Prove the following: (sin x + sin 3x) / (cos x + cos 3x) = tan 2x

Solution:

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

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

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

= sin 2x / cos 2x

= tan 2x

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 19

Prove the following: (sin x + sin 3x) / (cos x + cos 3x) = tan 2x

Summary:

We got, (sin x + sin 3x) / (cos x + cos 3x) = tan 2x. Hence Proved