# Proving Trigonometric Identities Calculator

## Get detailed solutions to your math problems with our Proving 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 proving trigonometric identities

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

Multiplying the fraction by $-1$

$\frac{1}{\cos\left(x\right)}+\frac{-\cos\left(x\right)}{1+\sin\left(x\right)}=\tan\left(x\right)$
3

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

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

When multiplying two powers that have the same base ($\cos\left(x\right)$), you can add the exponents

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

Apply the trigonometric identity: $1-\cos\left(x\right)^2$$=\sin\left(x\right)^2 \frac{\sin\left(x\right)^2+\sin\left(x\right)}{\cos\left(x\right)\left(1+\sin\left(x\right)\right)}=\tan\left(x\right) 6 Factor the polynomial \sin\left(x\right)^2+\sin\left(x\right) by it's GCF: \sin\left(x\right) \frac{\sin\left(x\right)\left(\sin\left(x\right)+1\right)}{\cos\left(x\right)\left(1+\sin\left(x\right)\right)}=\tan\left(x\right) 7 Simplify the fraction \frac{\sin\left(x\right)\left(\sin\left(x\right)+1\right)}{\cos\left(x\right)\left(1+\sin\left(x\right)\right)} by \sin\left(x\right)+1 \frac{\sin\left(x\right)}{\cos\left(x\right)}=\tan\left(x\right) 8 Apply the trigonometric identity: \frac{\sin\left(x\right)}{\cos\left(x\right)}$$=\tan\left(x\right)$

$\tan\left(x\right)=\tan\left(x\right)$
9

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

true