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Question

If cos θ+sin θ=cos θ, then what is the value of cos θsin θ? [3 MARKS]

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Solution

Formula: 1 Mark
Application: 2 Marks

cos θ+sin θ=2 cos θ

(cos θ+sin θ)2=(2 cos θ)2

cos2 θ+sin2 θ+2 sin θ cos θ=2 cos2 θ

1+2 sin θ cos θ=2 cos2 θ

2 sin θ cos θ=2 cos2 θ1 ..........(1)

( cos θ sin θ)2=cos2 θ+sin2 θ2 sin θ cos θ

=12 sin θ cos θ

=12 cos2 θ+1

=22 cos2 θ

=2(1cos2 θ)

=2 sin2 θ

(cos θsin θ)2=2 sin2 θ

cos θsin θ=2 sin θ

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