This question is from trigonometry topic trigonometric identities in which we have to show that
sin^2 θ + cos^4 θ = cos^2 θ + sin^4 θ
RS Aggarwal, Class 10, chapter 13A, question no 17(ii)
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sin^2 θ+cos^4 θ=cos^2θ+sin^4θ
L.H.S.=sin^2 θ+cos^4 θ
=(1−cos^2 θ)+cos^4 θ
=cos^4 θ−cos^2 θ+1
=cos^2 θ(cos^2 θ−1)+1
=cos^2 θ(−sin^2 θ)+1
=1−sin^2 θ cosθ
Now,
R.H.S.=cos^2 θ+sin^4 θ
=(1−sin^2 θ)+sin^4 θ
=sin^4 θ−sin^2 θ+1
=sin^2 θ(sin^2 θ−1)+1
=sin^2 θ(−cos^2 θ)+1
=1−sin^2 θ cos^2 θ
∴L.H.S.=R.H.S.