Question

(1+SINX)^(1/2) 1+sinx
-------------= -------
(1-sinx)^(1/2) |cosx|

Answer 1

verify

Answer 2

okay, you have what exactly? this?
\[\sqrt{\frac{1+sinx}{1-sin(x)}}=\frac{1+sin(x)}{|cos(x)|}\text{?}\]

Answer 3

correct

Answer 4

multiply top and bottom by conjugate: sqrt(1+sin x)
\[\frac{\sqrt{1+sinx}}{\sqrt{1-sinx}}*\frac{\sqrt{1+sinx}}{\sqrt{1+sinx}} = \frac{1+sinx}{\sqrt{1-\sin^{2} x}} = \frac{1+sinx}{cosx}\]

Answer 5

rationalise the denominator by multiplying by 1 + sin(x)

will result in

\[\sqrt{(1+\sin(x)^2/1 - \sin^2(x)}\]

denominator is cos^2(x) while square root of the numerator is (1+sin(x)

Answer 6

after the sqrt gets off the top wouldn't it go off the bottom as well

Answer 7

the reason its absolute value is that the square root will give a positive and negative answer.. hence the abs value