Yes indeed. That's a true statement.
Let's just work on the left side, and leave the right side alone.
The left side is cos² - sin² .
Do you remember the trig identity that says cos² + sin² = 1 ?
Take that and subtract sin² from each side of it: cos² = 1 - sin²
Now substitute that into the left side of the problem:
Left side: cos² - sin²
Substitute: (1 - sin²) - sin²
Remove parentheses: 1 - sin² - sin²
Combine like terms: 1 - 2 sin²
Now compare that to the right side of the problem.