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Question
Prove the following:
cos4θ − sin4θ +1= 2cos2θ
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Solution
L.H.S. = cos4θ − sin4θ +1
= (cos2θ)2 − (sin2θ)2 + 1
= (cos2θ + sin2θ)(cos2θ − sin2θ) + 1
= (1) (cos2θ − sin2θ) + 1
= cos2θ + (1 – sin2θ)
= cos2θ + cos2θ
= 2cos2θ
= R.H.S.
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