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Question

Given cotθ=78, then evaluate (i)(1+sinθ)(1sinθ)(1+cosθ)(1cosθ) (ii) (1+sinθ)cosθ

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Solution

(i) (1+sinθ)(1sinθ)(1+cosθ)(1cosθ)

=1sin2θ1cos2θ

=cos2θsin2θ=cot2θ=(78)2=4964

(ii) cotθ=78

tanθ=87

sec2θ=1+tan2θ

secθ=1137

(1+sinθ)cosθ=1cosθ+sinθcosθ=secθ+tanθ=1137+87=8+1137



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