Question

hey mate solve my question

Answer 1

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ANY DOUBT YOU CAN ASK ME.......

AND ALL THE BEST FOR YOUR EXAM....

Answer 2

✍HERE IS YOUR SOLUTION...⤵⤵
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$\bold{\underline{\underline{SOLUTION}}}$ ➡

$\bold{\underline{\red{We \: \: know \: \: that :- }}}$

$cosec {}^{2} A = 1 + cot {}^{2} A \\ \\ = > 1 + cot {}^{2} A = cosec {}^{2} A \\ \\ = > 1 = cosec {}^{2} A - cot {}^{2} A \: \: \: - - - - - - - > (1)$

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$\bold{\underline{\red{To \: \: Prove \: : -}}}$

$\boxed{\frac{cos \: A - sin \: A + 1}{cos \: A + sin \: A - 1} = cosec \: A + cot \: A}$

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$\underline{\bold{\red{Proof \: :-}}}$

$L.H.S. \: = \frac{cos \: A - sin \: A + 1}{cos \: A + sin \: A - 1} \\ \\ = \frac{ \frac{cos \: A}{sin \: A} - \frac{sin \: A}{sin \: A} + \frac{1}{sin \: A} }{ \frac{cos \: A}{sin \: A} + \frac{sin \: A}{sin \: A} - \frac{1}{sin \: A} } \\ \\ = \frac{cot \: A - 1 + cosec \: A}{cot \: A + 1 - cosec \: A} \\ \\ = \frac{cot \: A + cosec \: A - (cosec {}^{2} A - cot {}^{2} A)}{cot \: A + 1 - cosec \: A} \: \: \: \: \: \:[ From \: \: (1) ]\\ \\ = \frac{cot \: A + cosec \: A - [(cosec \: S + cot \: A)(cosec \: A - cot \: A)]}{cot \: A + 1 - cosec \: A} \\ \\ = \frac{(cosec \: A + cot \: A)(1 - cosec \: A + cot \: A}{1 - cosec \: A + cot \: A} \\ \\ = cosec \: A + cot \: A \\ \\ = R.H.S.$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{\underline{Proved.}}$

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$\bold{\underline{\red{Note \: : -}}} \: \: \: \: \: \boxed{cot \: A = \frac{cos \: A}{sin \: A} \:, \: cosec \: A \: = \frac{1}{sin \: A}}$

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