Multiple Angles

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The formula for sin 2θ is

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1. **Derive from Addition Formula**: Start with $\sin(A+B) = \sin A \cos B + \cos A \sin B$.
2. **Angle Equality**: Put $A = 	heta$ and $B = 	heta$.
3. **Substitution**: 
   - $\sin(	heta + 	heta) = \sin 	heta \cos 	heta + \cos 	heta \sin 	heta$
   - $\sin 2	heta = 2 \sin 	heta \cos 	heta$.
4. **Extension**: Can also be written as $\frac{2 	an 	heta}{1 + 	an^2 	heta}$.

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The formula cos 2θ can be written as

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