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# 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

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