What is the value of the following in items of trigonoetric ratios? sinA/(1+cosA) + (1+cosA)/sinA

What is the value of the following in items of…

What is the value of the following in items of trigonoetric ratios?

$\frac{sinA}{1+cosA}$ + $\frac{1+cosA}{sinA}$

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 2cosec A

Given that

$\frac{sinA}{1+cosA}$ + $\frac{1+cosA}{sinA}$

= (sin²A + 1 + cos²A + 2 cosA)/[sinA (1 + cosA)]

= (2 + 2 cosA)/[sinA * (1 + cosA)]

= 2/sinA = 2 cosecA