Trigonometric Identities Calculator

Solved example of trigonometric identities

Applying the trigonometric identity: $\tan(x)^2+1=\sec(x)^2$

Apply the trigonometric identity: $\csc\left(x\right)^2$$=1+\cot\left(x\right)^2$

Recognize that the trinomial $\tan\left(x\right)^2+2+\cot\left(x\right)^2$ is perfect square, so we can rewrite it as $\left(\tan\left(x\right)+\cot\left(x\right)\right)^2$

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

Apply the trigonometric identity: $\cot(x)=\frac{\cos(x)}{\sin(x)}$

Combine fractions with different denominator using the formula: $\displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}$

Applying the pythagorean identity: $\sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1$

The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

The power of a product is equal to the product of it's factors raised to the same power

Since both sides of the equality are equal, we have proven the identity