Question

prove that 1+costheta/sin²theta=1/1-costheta​

Answer 1

$lhs = \frac{1 + cos}{ {sin}^{2} }$

$= \frac{1 + cos}{1 - {cos \: }^{2} } \: \: \: \: ( {sin \: }^{2} = 1 - {cos \: }^{2} )$

$= \frac{1 + cos}{ {1 \: }^{2} - {cos \: }^{2} }$

$= \frac{1 + cos}{(1 + cos)(1 - cos)} \: \: \: \: ( {x}^{2} - {y}^{2} = (x + y)(x - y)$

$= \frac{1}{1 - cos}$

= RHS

Therefore ,,,,

LHS = RHS

Hence proved ....

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