# How do you prove that #sinytany=cosy# is not an identity by showing a counterexample?

##### 1 Answer

Jan 29, 2017

It is not an identity. See explanation.

#### Explanation:

We have

#sinytany=cosy#

This can be written as

#siny*siny/cosy=cosy" "# (#tany=siny/cosy# )

Solving this we get

#sin^2y=cos^2y#

This will be true only when

For example,

As a counterexample, we can say

but

Hope that helps!