Here, we show you a step-by-step solved example of trigonometry. This solution was automatically generated by our smart calculator:
Use the odd-even identity $\cos(-\theta)=\cos(\theta)$
Start by simplifying the left side of the identity: $-\cos\left(-x\right)+\sec\left(x\right)$
Starting from the left-hand side (LHS) of the identity
Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
Combine all terms into a single fraction with $\cos\left(x\right)$ as common denominator
When multiplying two powers that have the same base ($\cos\left(x\right)$), you can add the exponents
Combine all terms into a single fraction with $\cos\left(x\right)$ as common denominator
Apply the trigonometric identity: $1-\cos\left(\theta \right)^2$$=\sin\left(\theta \right)^2$
Rewrite the exponent $\sin\left(x\right)^2$ as a product of $\sin\left(x\right)$
Separating the fraction's numerator
Apply the trigonometric identity: $\frac{\sin\left(\theta \right)}{\cos\left(\theta \right)}$$=\tan\left(\theta \right)$
Rewrite $\frac{\sin\left(x\right)^2}{\cos\left(x\right)}$ as $\tan\left(x\right)\sin\left(x\right)$ by applying trigonometric identities
Since we have reached the expression of our goal, we have proven the identity
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