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.

\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)

\frac{\left(1+sin\left(\theta\:\right)\right)}{cos\theta\:}=\left(\frac{cos\left(\theta\:\right)}{1-sin\left(\theta\:\right)}\right)

\sec^20=1+\sin^20\sec^20

\frac{1+sec^2x}{sec^2x-1}-1=2cot^2x

\frac{cos\left(x\right)-sin\left(x\right)}{\cos\left(x\right)+sin\left(x\right)}=\frac{cos\left(2x\right)}{1+sin\left(2x\right)}

-tan\:\left(t\right)-\frac{cos\:\left(t\right)}{sin\:\left(t\right)-1}=sec\:\left(t\right)

\frac{\csc\left(x\right)^3+\sin\left(x\right)^3}{\csc\left(x\right)+\sin\left(x\right)}=\csc\left(x\right)^2-1+\sin\left(x\right)^2

tan\left(x\right)=\frac{sen\left(x\right)}{\sqrt{cos^2x}}

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