Question

prove: sec theta-1÷sec theta+1=(cot theta - cosec theta)^

Answer 1

This is the answer. It help you .

Answer 2

$LHS = \frac{(sec \theta - 1)}{(sec \theta + 1)} \\= \frac{(sec \theta - 1)(sec \theta - 1)}{(sec \theta + 1)(sec \theta -1)} \\= \frac{(sec \theta - 1)^{2}}{sec^{2} \theta - 1^{2} } \\= \frac{(sec \theta - 1)^{2}}{tan^{2} \theta}$

$\boxed { \pink { Since, sec^{2} \theta - 1 = tan^{2} \theta}}$

$= \Big( \frac{sec \theta - 1}{tan \theta }\Big)^{2}$

$= \Big( \frac{sec \theta}{tan \theta }- \frac{ 1}{tan \theta }\Big)^{2}$

$= \Big( \frac{\frac{1}{cos \theta}}{\frac{sin \theta}{cos \theta}} - cot \theta \Big)^{2}$

$= \Big( \frac{1}{sin \theta } - cot \theta \Big)^{2} \\= ( Cosec \theta - cot \theta )^{2} \\= RHS$

$Hence \:proved$

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