# How do you prove #csc^2(theta)(1-cos^2(theta)=1#?

##### 2 Answers

May 4, 2016

see below

#### Explanation:

Left Side:

May 4, 2016

First, we start with

#csc^2theta(1-cos^2theta) = 1,#

and consider what identities make sense to use. Note that

That means it would be convenient to have

#sin^2theta + cos^2theta = 1#

is a trig identity we can use. Therefore, we have

#csc^2theta(sin^2theta) = 1/cancel(sin^2theta)cancel(sin^2theta) = color(blue)(1)#