Math, asked by vigi7161, 1 year ago

Prove that this is true.

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Answered by Anonymous

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$\frac{cos \: a \: - sin \: a \: + 1}{cos \: a + sin \: a \: - 1} = \frac{cos \: a - sin \: a + 1}{sin \: a} \div \frac{cos \: a + sin \: a - 1}{sin \: a} \\ \\ \frac{cot \: a - 1 + cosec \: a}{cot \: a - cosec \: a} \\ \\ \frac{cot \: a \: + cosec \: a - ( {cosec}^{2} \: a \: - {cot}^{2} \: a )}{cot \: a \: - cosec \: a + 1} \\ \\ \frac{cot \: a \: + cosec \: a - (cosec \: a \: + cot \: a)(cosec \: a \: - cot \: a)}{cot \: a \: - cosec \: a \: + 1} \\ \\ \frac{(cosec \: a \: + cot \: a)(1 - cosec \: a + cot \: a)}{cot \: a \: - cosec \: a + 1} \\ \\ cosec \: a \: + cot \: a \\ \\ = rhs$

Anonymous: hope this is helpful for u

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