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if sec theta +tan theta=p,find the value of cosec theta

 Feb 7, 2019
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\(\sec \theta + \tan \theta = p\\ \sec^2 \theta - \tan^2 \theta = p (\sec \theta - \tan \theta)\\ \sec \theta - \tan \theta = \dfrac{1}{p}\\ 2 \sec \theta = p + \dfrac{1}{p}\\ \sec \theta = \dfrac{p^2 + 1}{2p}\\ \cos \theta = \dfrac{2p}{p^2 + 1}\\ \sin \theta = \sqrt{1 - \left(\dfrac{2p}{p^2 +1}\right)^2} = \dfrac{1-p^2}{1+p^2}\\ \color{red}\boxed{\csc \theta = \dfrac{1+p^2}{1-p^2} }\)

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 Feb 7, 2019

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