Question

please answer this i asked this question 3 times in my account my points are wasting please give me an appropriate step by step long answer please help me
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Answer 1

$LHS = \frac{(sin \theta + cos \theta)}{(sin \theta - cos \theta )} + \frac{(sin \theta - cos \theta)}{(sin \theta + cos \theta )} \\= \frac{(sin\theta + cos \theta )^{2} + (sin \theta - cos \theta)^{2}}{(sin \theta - cos \theta )(sin \theta + cos \theta)} \\= \frac{2(sin^{2} \theta + cos^{2}\theta)}{sin^{2} \theta - cos^{2} \theta }$

/* We know that, */

$\blue{ (a+b)^{2} + (a-b)^{2} = 2(a^{2} + b^{2}) }$

$= \frac{ 2 \times 1 }{ sin^{2}\theta - (1 - sin^{2} \theta )}$

$\boxed{ \pink{ \because sin^{2} \theta + cos^{2} \theta = 1 }}$

$= \frac{2}{sin^{2} \theta - 1 + sin^{2} \theta }\\= \frac{2}{2sin^{2} \theta - 1 } \\= RHS$

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