Prove the following: cos (3π/4 + x) - cos (3π/4 - x) = -√2 sin x

Solution:

LHS = cos (3π/4 + x) - cos (3π/4 - x)

= -2 sin [{(3π/4 + x) + (3π/4 - x)} / 2] sin [{(3π/4 + x) - (3π/4 - x)} / 2]

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

= -2sin (3π/4) sin (2x/2)

= -2sin (π - π/4) sin x     

= -2sin (π/4) sin x 

 [As sin (π - A) = sin A]

= -2 × 1/√2 × sin x 

 (by trigonometric table)

= -√2 sin x

= RHS

NCERT Solutions Class 11 Maths Chapter 3 Exercise 3.3 Question 11

Prove the following: cos (3π/4 + x) - cos (3π/4 - x) = -√2 sin x

Summary:

We got,cos (3π/4 + x) - cos (3π/4 - x) = -√2 sin x, Hence Proved