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Question

Choose the correct answer from the alternatives given.
If sinθ,+cosθ=p and secθ,+cosecθ=q. then q(p2 1) = ?

A
p
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B
2p
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C
3p
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D
2p2
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Solution

The correct option is B 2p
q(p21)=(secθ+cosecθ)(sinθ+cosθ)21)

=(1cosθ+1sinθ){sin2θ+cos2θ+2sinθcosθ1}

= (sinθ+cosθsinθcosθ)(1+2sinθcosθ1)

= (sinθ+cosθsinθcosθ)(2sinθcosθ)

=2(sinθ+cosθ) =2p

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