Math, asked by SmileQueen, 1 year ago

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Answers

Answered by Anonymous
2
HOPE ITS HELP YOU......
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Answered by TRISHNADEVI
11
✍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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