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Question

Prove that sin4 θcos4 θ=12 cos2 θ [3 MARKS]

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Solution

Formula: 2 Marks
Application: 1 Mark

Consider

sin4 θcos4 θ=(sin2 θ)2(cos2 θ)2

a2b2=(a+b)(ab)

=(sin2 θ+cos2 θ)(sin2 θcos2 θ)

=1(sin2 θcos2 θ) [sin2 θ+cos2 θ=1]

=sin2 θcos2 θ

=(1cos2 θ)cos2 θ [sin2 θ=1cos2 θ]

=12cos2 θ


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