Question

solve this question​

Answer 1

Answer:

Rationalisation

Step-by-step explanation:

First Rationalise it then use trigonometry equation.

Answer 2

Step-by-step explanation:

$\sqrt{ \frac{1 -cos \: A}{1 + cos \: A} } + cot\: A = cosec\: A \\ \\ LHS = \sqrt{ \frac{1 -cos \: A}{1 + cos \: A} } + cot\: A \\\\ = \sqrt{ \frac{1 -cos \: A}{1 + cos \: A} } \times \sqrt{ \frac{1 -cos \: A}{1 -cos \: A} } + cot\: A\\(Multiplying \:Numerator \: \&\: Denominator\:\\by \:\sqrt{1 -cos \: A}) \\ \\= \sqrt{ \frac{(1 -cos \: A)^{2} }{1 ^{2} - cos^{2} \: A} } + cot\: A \\ \\= \sqrt{ \frac{(1 -cos \: A)^{2} }{1 - cos^{2} \: A} } + cot\: A \\\\ = \sqrt{ \frac{(1 -cos \: A)^{2} }{sin^{2} \: A} } + cot\: A \\ \\= { \frac{(1 -cos \: A)}{sin \: A} } + cot\: A\\ \\ = \frac{1}{sin \: A} - \frac{cos \: A}{sin \: A} + cot\: A \\\\ = cosec \: A - cot\: A + cot\: A \\\\ = cosec \: A \\ \\= RHS \\ \\Hence \: Proved.$