What is the value of the following in terms of trigonometric ratios?
$\frac{sinA}{1+cosA}+\frac{1+cosA}{sinA}$
Answer & explanation
Correct answer: option 1
\(\frac{ sinA}{1 + cosA}\) + \(\frac{ 1 + cosA}{sinA}\)
= \(\frac{ sin²A + ( 1 + cos A )²}{sinA(1 + cosA)}\)
= \(\frac{ sin²A + 1 + cos² A + 2cosA}{sinA(1 + cosA)}\)
{ using , sin²A + cos²A = 1 }
= \(\frac{ 1 + 1 + 2cosA}{sinA(1 + cosA)}\)
= \(\frac{2( 1 + cosA)}{sinA(1 + cosA)}\)
= 2 cosecA