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Question

Show that cos3θsin3θ+sin3θcos3θ=34sin4θ.

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Solution

cos3θsin3θ+sin3θcos3θ

using trigonometric identities and simplifying

=(cos3θ+3cosθ4)sin3θ+(3sinθsin3θ4)cos3θ

=14(sin3θcos3θ+3cosθsin3θ+3sin3θcosθsin3θcos3θ)

=14(3cosθsin3θ+3sin3θcosθ)=34sin4θ

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