Question

$cosec\Delta =2,\frac{1}{tan\Delta }+\frac{sin\Delta }{1+cos\Delta }=?$

Answer 1

given that, $\cos ec\Delta =2$

consider, $\frac{1}{\tan \Delta }+\frac{\sin \Delta }{1+\cos \Delta }$

$=\frac{\cos \Delta }{\sin \Delta }+\frac{\sin \Delta }{1+\cos \Delta }$

$=\frac{\cos \Delta +{\cos }^2\Delta +{\sin }^2\Delta }{\sin \Delta \left(1+\cos \Delta \right)}$

$=\frac{\cos \Delta +1}{\sin \Delta \left(1+\cos \Delta \right)}$

${\sin }^2\Delta +{\cos }^2\Delta =1$

$\cos ec\Delta =2$