Answer :

Consider L.H.S. = sin2 θ + cos4 θ

= (sin2 θ) + (cos2 θ)2


= (sin2 θ) + (1 – sin2 θ)2


= (sin2 θ) + 1 + sin4 θ – 2sin2 θ


= 1 – sin2 θ + sin4 θ


= cos2 θ + sin4 θ


= R.H.S.


Hence, proved.


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