# Trigonometric Identities Calculator

## Get detailed solutions to your math problems with our Trigonometric Identities step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

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### Difficult Problems

1

Solved example of trigonometric identities

$\sec\left(x\right)^2+\csc\left(x\right)^2=\frac{1}{\sin\left(x\right)^2\cdot\cos\left(x\right)^2}$
2

Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

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

Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$

$\frac{1}{\cos\left(x\right)^2}+\frac{1}{\sin\left(x\right)^2}=\frac{1}{\sin\left(x\right)^2\cos\left(x\right)^2}$
4

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

$\frac{\sin\left(x\right)^2+\cos\left(x\right)^2}{\cos\left(x\right)^2\sin\left(x\right)^2}=\frac{1}{\sin\left(x\right)^2\cos\left(x\right)^2}$
5

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

$\frac{1}{\cos\left(x\right)^2\sin\left(x\right)^2}=\frac{1}{\sin\left(x\right)^2\cos\left(x\right)^2}$
6

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

true