Question

prove that (sintheta/1+costheta. ) +(1+costheta/sintheta). = 2cosectheta​

Answer 1

$\frac{sin \theta}{1 + cos \theta} + \frac{1 + cos \theta}{sin \theta} \\ \\ = \frac{ {sin}^{2} \theta + ( {1 + cos \theta})^{2} }{sin \theta(1 + cos \theta)} \\ \\ = \frac{2 + 2cos \theta}{sin \theta(1 + cos \theta)} \\ \\ = \frac{2}{sin \theta} \\ \\ = 2cosec \theta$