Please help me to solve this problem on how to proof if it is a double angle
$$\begin{align*} \cos 2 A &= 1-2\sin^2A\\ \sin 2 A &= 2\sin A\cos A\\ \tan 2A &=2\sin A\cos A\\ \end{align*}$$
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Exists two basic identities for sum of angles and they are $$\sin(A+B)=\sin A\cos B+\sin B\cos A$$ $$\cos(A+B)=\cos A\cos B-\sin A\sin B$$ if in these you put $A=B$ you get $$\sin(2A)=2\sin A\cos A$$ $$\cos(2A)=\cos^2 A-\sin^2 A$$ then you need to manipulate following identities $$\tan A=\frac{\sin A}{\cos A}$$ $${\sin^2 A}+{\cos^2 A}=1$$ |
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