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Question

Determine whether the following equation is identity or not:

sin4θ+cos4θ=1-2sin2θcos2θ.


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Solution

Verify L.H.S and R.H.S at any value of θ

sin4θ+cos4θ=1-2sin2θcos2θ

Let, L.H.S.=sin4θ+cos4θ

when θ=30

L.H.S.=sin430+cos430

=124+324=116+916=1016=58

R.H.S.=1-2sin230cos230

=1-2122×322=1-2×14×34=1-38=58

L.H.S.=R.H.S.

Hence, the given equation is an identity.


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