Question

Prove that :

(Cosec A - Cot A)^2 = (1-cosA)/(1+cosA)​

Answer 1

Answer:

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refer to attachment ..........

Answer 2

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TO PROVE :

${(cosec A \: - \: cotA )}^{2} = \: \frac{1 \: - \: cos A }{1 \: + \: cos A}$

L. H.S,

$= \: ({cosec A \: - \: cot A )}^{2}$

$= \: {( \frac{1}{sinA\:} \: - \: \frac{cos A }{sinA }) }^{2}$

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

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

$= \: \frac{(1 \: - \: cos A )(1 \: - \: cos A)}{(1 \: + \: cos A)(1 \: - \: cos A)}$

$= \: \frac{1 \: - \: cos A }{1 \: + \: cosA }$

$= \: RHS$

Hence Proved.