# Verify Ident.

• Jul 28th 2008, 07:26 PM
Casas4
Verify Ident.
Verify:
Square root(1+sin(x)/1-sin(x))=1+sin(x)/absolute value(cos(X))
Hopefully that made some since explained in words:
The Square Root (of the entire left side of equal sign) 1+sin(x) over 1-sin(x) equals 1 + sin(X) over the absolute value of cos(x)
Thanks
AC
• Jul 28th 2008, 10:08 PM
mr fantastic
Quote:

Originally Posted by Casas4
Okay so i am completely stuck and hopefully you can understand this

Square root (of the whole thing on left side of = sign) (1+sin(x)/1-sin(x)) = 1+sin(x)/Absolute value cos (x)
If that didnt make since im sorry
THanks
AC

Left hand side = $\displaystyle \sqrt{\frac{1 + \sin x}{1 - \sin x}} = \sqrt{\frac{(1 + \sin x)(1 + \sin x)}{(1 - \sin x)(1 + \sin x)}}$

$\displaystyle = \sqrt{\frac{(1 + \sin x)^2}{1 - \sin^2 x}} = \sqrt{\frac{(1 + \sin x)^2}{\cos^2 x}}$

$\displaystyle = \frac{\sqrt{(1 + \sin x)^2}}{\sqrt{\cos^2 x}}$

$\displaystyle = \frac{1 + \sin x}{|\cos x|}$

since $\displaystyle 1 + \sin x \geq 0$ for all values of x but $\displaystyle -1 \leq \cos x \leq 1$.