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

Question

asked Feb 22, 2019 167k views

1 Answer

Hmhensen · Answer 1 · 2019-02-25T20:03:10+0000

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)