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Question

Is LHS=RHS?

tan2θ1+tan2θ+cot3θ1+cot2θ=secθsinθ2cosecθcosθ
Say true or false.

A
True
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B
False
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C
Ambiguous
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D
Data insufficient
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Solution

The correct option is B False
cot3x1+cot2x
=tan2(x).cot3x1+tan2(x)
=cot(x)1+tan2(x)
Hence the above expression becomes,
tan2x+cotx1+tan2(x)
=tan3x+1(tanx)(tan2x+1)
=cos3(x)(sin3x+cos3x)cos3x.sinx
=cos3x+sin3xsinx
RHS
=12sin2xcos2xsinx.cosx
=(sin2x+cos2x)22sin2xcos2xsinx.cosx
=sin4x+cos4xsinx.cosx
Hence LHSRHS

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