Question

1+cos a/1 - cos a =(cosec a +cot a)^2 ​

Answer 1

Answer:

$taking \: left \: hand \: side \\ \\ by \: rationalising \\ \\ \frac{1 + cos \: a}{1 - cos \: a} \times \frac{1 + cos \: a}{1 + cos \: a} \\ \\ = \frac{ {(1 + cos \: a)}^{2} }{ {(1)}^{2} - {(cos \: a)}^{2} } \\ \\ = \frac{ {(1 + cos \: a)}^{2} }{1 - {cos}^{2} a} \\ \\ = \frac{ {(1 + cos \: a)}^{2} }{ {sin }^{2} a} \\ \\ = ( \frac{1 + cos \: a}{sin \: a} )^{2} \\ \\ = ( \frac{1}{sin \: a} + \frac{cos \: a}{sin \: a} )^{2} \\ \\ = (cosec \: a + cot \: a)^{2} \\ \\ = right \: hand \: side$

Step-by-step explanation:

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