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Question

Prove the following: 

cos(3π4+x)cos(3π4x)=2sin x


Solution

We have 

L.H.S. = cos (3π4+x) - cos (3π4x)  

=-2 sin 3π4sin x

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

=- 2 sin (ππ4) sin x

=- 2 sin π4 sin x 

[ sin (πθ) = sin θ]

=- 2×12 sin x

=- 2 sin x = R.H.S. 
 

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