Question

Prove that cos(3π/4+x)-cos(3π/4-x)=-√2sinx

Answer 1

Given, cos(3pi/4+x)-cos(3pi/4-x) can be written as,

= cos 3pi/4 cos x - sin 3pi/4sinx - (cos 3pi/4cos x + sin 3pi/4sin x)

= cos 3pi/4 cos x - sin 3pi/4sin x - cos 3pi/4 cos x - sin 3pi/4 sin x

= -2sin 3pi/4 sin x

= -2 * (1/root 2) sin x

= -root 2 sin x

Answer 2

Thank you for asking this question

Here is your answer:

L.H.S. = Cos(3π/4+x)-cos(3π/4-x)

= cos 3π/4 cos x - sin 3π/4 sin x - [cos 3π/4 cos x + sin 3π/4 sin x]

= cos 3π/4 cos x - sin 3π/4 sin x - cos 3π/4 cos x - sin 3π/4 sin x]

= -2sin 3π/4 sin x

= -2 x (1/√2) sin x

= -√2sin x

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