Please submit your concern

Question:

If $\frac{1}{1-\sin \theta }$ + $\frac{1}{1+\sin \theta }$ = 4 sec θ, 0° < θ < 90°, then the value of cot θ + cosec θ is:

Explanation:

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

$\frac{1+\sin \theta + 1-\sin \theta }{1-{\sin }^2\theta }$ = $\frac{4}{\cos \theta }$

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

0° < θ < 90°

⇒ θ = 60°

cot θ + cosec θ = cot 60° + cosec 60°

= $\frac{1}{\sqrt{3}}$ + $\frac{2}{\sqrt{3}}$

= $\frac{3}{\sqrt{3}}$

= $\sqrt{3}$

Hence, the correct answer is Option B