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Question

Prove that

cosec θ(cosec θ1)+cosec θ(cosec θ+1)=2 sec2 θ [2 MARKS]

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Solution

Concept: 1 Mark
Application: 1 Mark

We have

=cosec θ(cosec θ1)+cosec θ(cosec θ+1)

=cosec θ(cosec θ+1)+cosec θ(cosec θ1)(cosec2 θ1)

=2 cosec2 θ(1+cot2 θ1) [cosec2 θ=1+cot2 θ]

=2 cosec2 θcot2 θ

=2 cosec2 θ tan2 θ

=2×1sin2 θ×sin2 θcos2 θ

=2cos2 θ

=2 sec2 θ

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