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Proving Trigonometric Identities


Definition

To prove a trigonometric identity, you have to show that one side of the equation can be transformed into the other side.

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Problems Solved

Prove the identity $\cos\left(\frac{3\pi}{2}-x\right)=-\sin x$
Prove the identity $\left(\sin\left(x\right)+\cos\left(x\right)\right)^2-1=2\sin\left(x\right)\cos\left(x\right)$
Prove the identity $\frac{\sec\left(\infty\right)}{\tan\left(\infty\right)+\cot\left(\infty\right)}=\sin\left(\infty\right)$
Prove the identity $\cot\left(a\right)+\frac{\sin\left(a\right)}{1+\cos\left(a\right)}=\csc\left(a\right)$
Prove the identity $\sin x=\cos x\tan x$
Prove the identity $\frac{\cos\left(x\right)}{1+\cos\left(2x\right)}=\frac{1}{2\cos\left(x\right)}$
Prove the identity $tg\left(270+a\right)=-cotg\left(a\right)$
Prove the identity $\cos^2A-sen^2A=1-2sen^2A$

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