Question

1+cosA / 1-cosA =(cotA-cosecA)^2

Answer 1

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Answer 2

$<font \: color = 'blue' >$

$\mathtt{hey \: mate \: here \: is \: ur \: ans}$


$\mathcal{solution}$

$\mathtt{as \: given}$

$\mathtt{ \frac{1 + cos \: a}{1 - cos \: a} = (cot \: a - cosec \: a) ^{2} } \\ \\ \mathtt{taking \: lhs} \\ \\ = > \mathtt{ \frac{1 + cos \: a}{1 - cos \: a} } \\ \\ = > \mathtt{ \frac{(1 + cos \: a)(1 + cos \: a)}{(1 - cos \: a)(1 + cos \: a)} } \\ \\ = > \mathtt{ \frac{(1 + cos \: a)^{2} }{ {1}^{2} - (cos \: a)^{2} } } \\ \\ = > \mathtt{ \frac{(1 + cos \: a)^{2} }{1 - cos^{2}a } } \\ \\ = > \mathtt{ \frac{(1 + cos \: a)^{2} }{sin^{2} a} } \\ \\ = > \mathtt{( \frac{1 + cosa}{sina} }) ^{2} \\ \\ = > \mathtt{ (\frac{1}{sin \: a} + \frac{cos \: a \: }{sin \: a})^{2} } \\ \\ = > \mathtt{(cosec \: a \: + cos \: a) ^{2} } \: \: ans$