Question

Find the value of 1+sinA /1-sinA whole root

Answer 1

Answer:

tan($\frac{\pi}{4}$+$\frac{A}{2}$)

Step-by-step explanation:

$\sqrt{\frac{1+sinA}{1-sinA} }$

$\sqrt{\frac{sin^2A+cos^2A+2sin\frac{A}{2}cos\frac{A}{2}}{sin^2A+cos^2A-2sin\frac{A}{2}cos\frac{A}{2}} }$

$\sqrt{\frac{(sin\frac{A}{2}+cos\frac{A}{2})^2}{(sin\frac{A}{2}-cos\frac{A}{2})^2} }$

$\frac{sin\frac{A}{2}+cos\frac{A}{2}}{sin\frac{A}{2}-cos\frac{A}{2}}$

Dividing both numerator and denominator by cos$\frac{A}{2}$, we get:

$\frac{1+tan\frac{A}{2}}{1-tan\frac{A}{2}}$

since, tan$\frac{\pi}{4}$ = 1, hence,

$\frac{tan\frac{\pi}{4}+tan\frac{A}{2}}{tan\frac{\pi}{4}-tan\frac{A}{2}}$

tan($\frac{\pi}{4}$+$\frac{A}{2}$)