Question

Simplify the expression 1/√(1-cos^2 x) . Remember cos x= 1/csc x

Answer 1

First, we are going to use the Pythagorean identity:
`sin^2(x)+cos^2(x)=1` to rewrite our expression. Solving for
`sin^2(x)` in our Pythagorean identity we get that
`sin^2(x)=1-cos^2(x)`, so we can rewrite our expression as follows:

`(1)/( √(1-cos^2(x)) ) = (1)/( √(sin^2(x)) ) = (1)/(sin(x))`

Next, we are going to use the trig identity:
`csc(x)= (1)/(sin(x))` to completely simplify our expression:

`(1)/(sin(x)) =csc(x)`

We can conclude that
`(1)/( √(1-cos^2(x)) )=csc(x)`