Simplify the trigonometric expression (cot(x)tan(x)^2)/sec(x)

 Exercise

$\frac{\cot\left(x\right)\tan\left(x\right)^2}{\sec\left(x\right)}$

 

Apply the trigonometric identity: $\tan\left(\theta \right)^n$$=\frac{\sin\left(\theta \right)^n}{\cos\left(\theta \right)^n}$, where $n=2$

$\frac{\cot\left(x\right)\frac{\sin\left(x\right)^2}{\cos\left(x\right)^2}}{\sec\left(x\right)}$

 Why is tan(x) = sin(x)/cos(x) ?

 

Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

$\frac{\cot\left(x\right)\frac{\sin\left(x\right)^2}{\cos\left(x\right)^2}}{\frac{1}{\cos\left(x\right)}}$

 

Simplify the fraction $\frac{\cot\left(x\right)\frac{\sin\left(x\right)^2}{\cos\left(x\right)^2}}{\frac{1}{\cos\left(x\right)}}$

$\cot\left(x\right)\frac{\sin\left(x\right)^2\cos\left(x\right)}{\cos\left(x\right)^2}$

 

Simplify the fraction by $\cos\left(x\right)$

$\cot\left(x\right)\frac{\sin\left(x\right)^2}{\cos\left(x\right)}$

$\cot\left(x\right)\frac{\sin\left(x\right)^2}{\cos\left(x\right)}$

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