Here, we show you a step-by-step solved example of trigonometry. This solution was automatically generated by our smart calculator:
Starting from the left-hand side (LHS) of the identity
Factor the polynomial $\tan\left(x\right)^2-\tan\left(x\right)^2\sin\left(x\right)^2$ by it's greatest common factor (GCF): $\tan\left(x\right)^2$
Apply the trigonometric identity: $1-\sin\left(\theta \right)^2$$=\cos\left(\theta \right)^2$
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$
Multiplying the fraction by $\cos\left(x\right)^2$
Simplify the fraction $\frac{\sin\left(x\right)^2\cos\left(x\right)^2}{\cos\left(x\right)^2}$ by $\cos\left(x\right)^2$
Multiplying the fraction by $\cos\left(x\right)^2$
Since we have reached the expression of our goal, we have proven the identity
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