Proving Trigonometric Identities Calculator

Solved example of proving trigonometric identities

Multiplying the fraction by $-1$

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

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

Apply the trigonometric identity: $1-\cos\left(x\right)^2$$=\sin\left(x\right)^2$

Factor the polynomial $\sin\left(x\right)^2+\sin\left(x\right)$ by it's GCF: $\sin\left(x\right)$

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 $\sin\left(x\right)+1$

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

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