Question

Solve $\frac{\cos \theta }{1-\sin \theta }+\frac{\cos \theta }{1+\sin \theta }=4$ for $\theta <90$

Answer 1

solve $\frac{cos\theta }{1-sin\theta }+\frac{cos\theta }{1+sin\theta }=4$ $\theta <90$

$\frac{cos\theta }{1-sin\theta }+\frac{cos\theta }{1+sin\theta }=4$

$\frac{cos\theta (1+sin\theta )+cos\theta (1-sin\theta )}{1-si{n}^2\theta }=4$

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

$\therefore \frac{2cos\theta }{co{s}^2\theta }=4$

$\therefore \frac{2}{4}=cos\theta$

$\therefore cos\theta =\frac{1}{2}$

$\therefore \theta ={60}^{\circ }$