Final Answer
Step-by-step Solution
Problem to solve:
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Applying the trigonometric identity: $\cot\left(\theta\right)=\frac{1}{\tan\left(\theta\right)}$
Combine all terms into a single fraction with $\tan\left(x\right)$ as common denominator
When multiplying two powers that have the same base ($\tan\left(x\right)$), you can add the exponents
Applying the trigonometric identity: $\tan(x)^2+1=\sec(x)^2$
Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
Simplify the fraction
Simplify the fraction by $\cos\left(x\right)$
Applying the trigonometric identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
The reciprocal sine function is cosecant: $\frac{1}{\sin(x)}=\csc(x)$
Since both sides of the equality are equal, we have proven the identity