Question

Prove that :


`cosec (alpha) - cot( alpha ) = √(1 - cost (\alpha) / ( \alpha )`
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Answer 1

Explanation:

R.H.S.=
`\sqrt{(1-cos\alpha )/(1+cos \alpha ) } \\=\sqrt{(1-cos\alpha )/(1+cos\alpha ) } * \sqrt{(1-cos\alpha )/(1-cos \alpha ) } \\=((√(1-cos\alpha ) )^2)/(√(1-cos^2 \alpha ) ) \\=(1-cos\alpha )/(√(sin^2\alpha ))\\ =(1-cos\alpha )/(sin \alpha ) \\=(1)/(sin \alpha ) -(cos\alpha )/(sin \alpha ) \\=cosec \alpha -cot \alpha \\=L.H.S.`