allery$\cos 2\theta$ equals:
A$1 - 2\sin^2\theta$
B$\sin^2\theta - \cos^2\theta$
C$2\sin\theta \cos\theta$
D$1 + 2\sin^2\theta$
Answer & Solution
Correct answer: A. $1 - 2\sin^2\theta$
Double-angle for cosine has three equivalent forms:
- $\cos 2\theta = \cos^2\theta - \sin^2\theta$ (definition from angle-sum)
- $\cos 2\theta = 1 - 2\sin^2\theta$ (replace $\cos^2 = 1 - \sin^2$)
- $\cos 2\theta = 2\cos^2\theta - 1$ (replace $\sin^2 = 1 - \cos^2$)
Option D is $\sin 2\theta$, not $\cos 2\theta$.
The $1 - 2\sin^2$ form is useful when solving equations involving $\cos 2\theta$ and $\sin\theta$ together.
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