multiple angles

Question

The formula cos 2θ can be written as

RankGuru · Accepted Answer

1. **Basic Double Angle**: $\cos 2	heta = \cos^2 	heta - \sin^2 	heta$.
2. **Transform using $\sin^2 	heta = 1 - \cos^2 	heta$**:
   - $\cos 2	heta = \cos^2 	heta - (1 - \cos^2 	heta) = 2\cos^2 	heta - 1$.
3. **Transform using $\cos^2 	heta = 1 - \sin^2 	heta$**:
   - $\cos 2	heta = (1 - \sin^2 	heta) - \sin^2 	heta = 1 - 2\sin^2 	heta$.
4. **Result**: All three expressions are mathematically identical and highly useful in calculus.

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The formula for sin 2θ is