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22 March, 08:04

Cos^theta - sin^2 theta = 1-2 sin^2 theta

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  1. 22 March, 08:26
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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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