hey mate solve my question
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ANY DOUBT YOU CAN ASK ME.......
AND ALL THE BEST FOR YOUR EXAM....
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![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. 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.](https://tex.z-dn.net/?f=L.H.S.+%5C%3A+%3D+%5Cfrac%7Bcos+%5C%3A+A+-+sin+%5C%3A+A+%2B+1%7D%7Bcos+%5C%3A+A+%2B+sin+%5C%3A+A+-+1%7D+%5C%5C+%5C%5C+%3D+%5Cfrac%7B+%5Cfrac%7Bcos+%5C%3A+A%7D%7Bsin+%5C%3A+A%7D+-+%5Cfrac%7Bsin+%5C%3A+A%7D%7Bsin+%5C%3A+A%7D+%2B+%5Cfrac%7B1%7D%7Bsin+%5C%3A+A%7D+%7D%7B+%5Cfrac%7Bcos+%5C%3A+A%7D%7Bsin+%5C%3A+A%7D+%2B+%5Cfrac%7Bsin+%5C%3A+A%7D%7Bsin+%5C%3A+A%7D+-+%5Cfrac%7B1%7D%7Bsin+%5C%3A+A%7D+%7D+%5C%5C+%5C%5C+%3D+%5Cfrac%7Bcot+%5C%3A+A+-+1+%2B+cosec+%5C%3A+A%7D%7Bcot+%5C%3A+A+%2B+1+-+cosec+%5C%3A+A%7D+%5C%5C+%5C%5C+%3D+%5Cfrac%7Bcot+%5C%3A+A+%2B+cosec+%5C%3A+A+-+%28cosec+%7B%7D%5E%7B2%7D+A+-+cot+%7B%7D%5E%7B2%7D+A%29%7D%7Bcot+%5C%3A+A+%2B+1+-+cosec+%5C%3A+A%7D+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A+%5C%3A%5B+From+%5C%3A+%5C%3A+%281%29+%5D%5C%5C+%5C%5C+%3D+%5Cfrac%7Bcot+%5C%3A+A+%2B+cosec+%5C%3A+A+-+%5B%28cosec+%5C%3A+S+%2B+cot+%5C%3A+A%29%28cosec+%5C%3A+A+-+cot+%5C%3A+A%29%5D%7D%7Bcot+%5C%3A+A+%2B+1+-+cosec+%5C%3A+A%7D+%5C%5C+%5C%5C+%3D+%5Cfrac%7B%28cosec+%5C%3A+A+%2B+cot+%5C%3A+A%29%281+-+cosec+%5C%3A+A+%2B+cot+%5C%3A+A%7D%7B1+-+cosec+%5C%3A+A+%2B+cot+%5C%3A+A%7D+%5C%5C+%5C%5C+%3D+cosec+%5C%3A+A+%2B+cot+%5C%3A+A+%5C%5C+%5C%5C+%3D+R.H.S.)

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