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Question

If sin 6θ=32 cos5 θ sin θ32 cos3 θ sin θ+3x, then x=

A
cos θ
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B
cos 2θ
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C
sin θ
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D
sin 2θ
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Solution

The correct option is D sin 2θ
sin 6θ=2 sin 3θ cos 3θ
=2[3 sin θ4 sin3 θ][4 cos3 θ3 cos3 θ]
=24 sin θ cos θ(sin2 θ+cos2 θ)18 sin θ cos θ32 sin2 θ cos2 θ
=32 cos5 θ sin θ32 cos3 θ sin θ+3 sin 2θ
On comparing, x=sin 2θ.

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