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1+cot square alpha/1+cosec alpha= cosec alpha

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1+cot square alpha/1+cosec alpha= cosec alpha

Posted by Anil Kumar 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

LHS {tex} = 1 + \frac{{{{\cot }^2}\theta }}{{1 + \cos ec\theta }}{/tex}
{tex} = 1 + \frac{{\cos e{c^2}\theta - 1}}{{1 + \cos ec\;\theta }}{/tex} {tex}\left[ {\because {{\cot }^2}\theta = \cos e{c^2}\theta - 1} \right]{/tex}
{tex} = 1 + \frac{{(\cos ec\theta + 1)(\cos ec\theta - 1)}}{{(1 + \cos ec\theta )}}{/tex} {tex}\left[ {\because {a^2} - {b^2} = (a + b)(a - b)} \right]{/tex}
{tex} = 1 + \cos ec\;\theta - 1{/tex}
{tex} = \cos ec\theta {/tex}
= RHS
Hence proved.

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CBSE > Class 10 > Mathematics

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Posted by Kanika . 1 month, 3 weeks ago

CBSE > Class 10 > Mathematics