Question

if cosec thetta + cot thetta=P then prove that cos thetta = p^-1/p^+1

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Answer 1

we know that cosec^2 theta -- cot^2 theta=1

(cosec theta +cot theta)(cosec theta -- cot theta) =1

cosec theta-- cot theta =1/p _____________> equation__ 2

adding the both equations gives 2 cosec theta =p +(1/p)

cosec theta =(p^2 +1)/2p

sin theta =2p/(p^2 +1)

by triangle we get adjacent side as p^2-- 1

cos theta = adj/ hyp

=p^2 --1/p^2 +1

HENCE proved

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