Cancel like terms $2\cos\left(x\right)^2$ and $-2\cos\left(x\right)^2$
$\frac{1}{\cos\left(x\right)}$
8
Applying the trigonometric identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
$\sec\left(x\right)$
9
Since we have reached the expression of our goal, we have proven the identity
true
Final answer to the problem
true
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In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined.