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

Solution:

LHS = (sin x - sin y) / (cos x + cos y)

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

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

= [sin (x - y) / 2] / [cos (x - y) / 2]

= tan (x - y) / 2

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 18

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

Summary:

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