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
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
Multiplying the fraction by $\sin\left(x\right)$
When multiplying two powers that have the same base ($\sin\left(x\right)$), you can add the exponents
Multiplying the fraction by $\sin\left(x\right)$
Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
Combine fractions with common denominator $\cos\left(x\right)$
Apply the trigonometric identity: $1-\sin\left(\theta \right)^2$$=\cos\left(\theta \right)^2$
Simplify the fraction $\frac{\cos\left(x\right)^2}{\cos\left(x\right)}$ by $\cos\left(x\right)$
Since we have reached the expression of our goal, we have proven the identity
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