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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 $\tan^2\left(x\right)\sec^2\left(x\right)-\sec^2\left(x\right)+1=\frac{1}{\cot^4\left(x\right)}$
Prove the identity $\tan\left(a+45\right)=\frac{1+\tan\left(a\right)}{1-\tan\left(a\right)}$
Prove the identity $\cot\left(a-b\right)=\frac{cot\left(a\right)cot\left(b\right)+1}{cot\left(b\right)-cot\left(a\right)}$
Prove the identity $\frac{\cos\left(x\right)\cos\left(x\right)}{1-\sin\left(x\right)}=1+\sin\left(x\right)$
Prove the identity $\frac{1-\sin^2\left(x\right)}{1-\sin\left(x\right)}=1+\sin\left(x\right)$
Prove the identity $tan\left(x\right)=\frac{sen\left(x\right)}{\sqrt{cos^2x}}$
Prove the identity $\frac{\csc^2\left(x\right)-\sin^2\left(x\right)}{\csc\left(x\right)+\sin\left(x\right)}=\cos\left(x\right)\cdot\cot\left(x\right)$

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$tan\left(x\right)=\frac{sen\left(x\right)}{\sqrt{cos^2x}}$ 7 views
$\frac{1-\sin^2\left(x\right)}{1-\sin\left(x\right)}=1+\sin\left(x\right)$ 5 views
$1-\frac{\tan^2\left(x\right)}{1+\tan^2\left(x\right)}=\cos^2\left(x\right)$ 3 views
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