Question

if $0<\theta <{90}^{\circ }$ and $\frac{\sin \theta }{1-\cos \theta }+\frac{\sin \theta }{1+\cos \theta }=4,$ then the value of $\theta$

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. none

Answer 1

Answer: (A)

${30}^{\circ }$

$\frac{\sin \theta }{1-\cos \theta }+\frac{\sin \theta }{1+\cos \theta }=4$
$\frac{sin\theta +\sin \theta \cos \theta +\sin \theta -\sin \theta \cos \theta }{co{s}^2\theta -1}=4$
$\frac{2\sin \theta }{{\sin }^2\theta }=4$
$\sin \theta =\frac{1}{2}$
$\sin \theta =\sin 30$
$\theta ={30}^{\circ }$