sin 4 theta + sin 2 theta x cos 2 theta = sin 2 theta
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Answer:
sin 2θ+cos 4 θ=cos 2θ+sin 4θ
L.H.S.
=sin 2θ+cos 4θ=(1−cos 2θ)+cos 4 θ
=cos 4θ−cos 2 θ+1
=cos 2 θ(cos 2 θ−1)+1
=cos 2 θ(−sin 2 θ)+1
=1−sin 2 θcosθ
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 2θ(sin 2θ−1)+1
=sin 2 θ(−cos 2θ)+1
=1−sin 2θcos 2 θ
∴L.H.S.=R.H.S.
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