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