Question

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

Answer 1

Step-by-step explanation:

$\frac{1 - \cos }{1 + \cos } = ( {cosec - \cot })^{2} \\ \\ \: \frac{1 - \cos }{1 + \cos } \times \frac{1 - \cos }{1 - \cos } ...........((multiply \: both \: with \: (1 - \cos))) \\ \\ \frac{(1 - \cos) {}^{2} }{ {1}^{2} - { \cos }^{2} } \\ \\ = \frac{ {1}^{2} - 2 \cos + { \cos }^{2} }{ { \sin }^{2} } .. (({1}^{2} + { \cos }^{2} = 1)) \\ \\ now \: give \: personal \: \: division \: \: \\ \frac{ {1}^{2} }{ { \sin }^{2} } - \frac{2 \cos}{ { \sin}^{2} } + \frac{ { \cos}^{2} }{ { \sin }^{2} } \\ \\ {cosec}^{2} - 2 \cot \times cosec + { \cot }^{2} \\ \\ (cosec - cot) {}^{2} \: \: \: \: \: \: ......from \: \: (a - b) {}^{2}$