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Mathematics
Villa
18 March, 21:15
Cos^theta - sin^2 theta = 1-2 sin^2 theta
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Nathan Lamb
19 March, 00:41
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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.
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