Question

sinA/1+cosA + 1+cosA/sinA =2cossecA​

Answer 1

Answer:

$lhs = \frac{sin \: a}{1 + cos \: a} + \frac{1 + cos \: a}{sin \: a} \\ \\ = \frac{ {(sin \: a)}^{2} + {(1 + cosa)}^{2} }{(1 + cos \: a)(sin \: a)} \\ \\ = \frac{ {sin}^{2}a + {cos}^{2} a + 1 + 2cos \: a }{(1 + cos \: a)(sin \: a)} \\ \\ = \frac{2 + 2cos \: a}{(1 + cos \: a)(sin \: a)} \\ \\ = \frac{2(1 + cos \: a)}{(1 + cos \: a)(sin \: a)} \\ \\ = 2 \times \frac{1}{sin \: a} \\ \\ = 2cosec \: a \\ \\ = rhs \\ proved \\ \\ = > ( {sin}^{2} a + {cos}^{2} a) = 1 \\ \\ = > \frac{1}{sina} = cosec \: a$