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Question

Prove that : sec(3π2θ)sec(θ5π2)+tan(5π2+θ)tan(θ3π2)=1


Solution

LHS=sec(3π2θ)sec(θ5π2)+tan(5π2+θ)tan(θ3π2)

=sec(3π2θ)sec((5π2θ))+tan(5π2θ)tan[(3π2θ)]

=cosecθ.sec(5π2θ)=cotθ×()tan(3π2θ)

⎢ ⎢ ⎢ ⎢(sec(3π2θ))=cosecθ,sec(θ)=secθ,tan(5π2+θ)=cotθand tan(θ)=(tanθ)⎥ ⎥ ⎥ ⎥

=cosecθ×cosecθcotθ×(1)×cotθ

(sec(5π2θ))=cosecθand tan(3π2θ)=cotθ

=cosec2θ×cot2θ

=cosec2θ×cosec2θ1[cosec2θ=1+cot2θ]

=-1 =RHS Hence proved.


Mathematics
RD Sharma
Standard XI

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