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Question

Question 4
(sin α+cos α)(tan α+cot α)=sec α+cosec α

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Solution

LHS=(sin α+cos α)(tan α+cot α)

=(sin α+cos α)(sin αcos α+cos αsin α) [tan θ=sin θcos θ and cot θ=cos θsin θ]

=(sin α+cos α)(sin2 α+cos2 αsin α.cos α) [sin2 θ+cos2 θ=1]

=1cos α+1sin α [sec θ=1cos θ and cosec θ=1sin θ]

=sec α+cosec α


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