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Question

Prove the following: 
cos 4x+ cos 3x + cos 2xsin 4x + sin 3x + sin 2x=cot 3x
 


Solution

We have 

L.H.S. = cos 4x+ cos 3x+ cos 2xsin 4x + sin 3x+ sin 2x

= (cos 4x+ cos 2x)+ cos 3x(sin 4x + sin 2x)+ sin 3x

= 2 cos4x+2x2cos4x2x2+cos 3x2 sin4x+2x2cos4x2x2+sin 3x

sin C+ sin D=2sin(C+D2)cos(CD2)cos C+ cos D=2 cos(C+D2)cos(CD2)

= 2 cos 3x cos x+ cos 3x2 sin 3x cos x + sin 3x

= cos 3x (2 cos x+1)sin 3x (2 cos x +1)=cos 3xsin 3x

= cot 3x = R.H.S. 


Mathematics

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