Question

Show that $\frac{\sin \theta }{1+\cos \theta }=\tan \frac{\theta }{2}$

Answer 1

L.H.S.

$\frac{\sin \theta }{1+cos\theta }$

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

$=\frac{2\sin \frac{\theta }{2}\cos \frac{\theta }{2}}{1+2{\cos }^2\frac{\theta }{2}-1}$

$=\frac{2\sin \frac{\theta }{2}\cos \frac{\theta }{2}}{2{\cos }^2\frac{\theta }{2}}$

$=\frac{\sin \frac{\theta }{2}}{\cos \frac{\theta }{2}}$

$=\tan \frac{\theta }{2}$

R.H.S.