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Example 1
$-\cos (2x) + \cos ^2 x$ is equivalent to
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$\sin^2 x$
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$-\cos^2 x$
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$-\cos (2x) \cdot \cos ^2 x$
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$\cos^2 x - \sin^2 x$
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$-2\cos x + \cos ^2 x$
Solution
- We first use the identity $\cos(2x)=\cos^2 x - \sin^2 x$ to substitute $\cos(2x)$ by $\cos^2 x - \sin^2 x$ in the given expression
$-\cos (2x) + \cos ^2 x=-(\cos^2 x - \sin^2 x)+\cos ^2 x$
- and simplify
$= -\cos^2 x + \sin^2 x+\cos ^2 x = \sin^2 x$
Answer A
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