Remember: to show an identity is true, you have to prove it for all values of a variable. In order to prove that an expression is false, you only need to show one value of the variable that doesn't work. This is called a counterexample.

Sometimes you have trigonometric equations that are true for some values, but not for others.

When you provide a counterexample, you are looking for a value which results in an inequality instead of an equality.

Example:

Provide a counterexample that proves the equation is not a trigonometric identity.

Procedure:

1. Simplify each side as much as possible using trigonometric identities where possible.

2. Find a value that can be substituted into the equation that makes it an inequality.

Solution:
sin0cos0=cos0/sin0
sin^2 0cos0=cos0
sin^2 0=cos0/cos0
sin^2 0=1


Find a value for θ so sin2 θ ≠ 1.
If 0=30,sin0 = 1/2 and (1/2)^2=1/4 = 1

The title of your post doesn't seem to match the problem you've worked out here. I assume your use of the characeter "0" iis meant to be , and you are giving an example to show that:



If so, this looks good. However, the angle you chose for your example (30 degrees) is in the 1st quadrant, not the 4th.