Simplify the trigonometric expression cos(a)^2+(cot(a)cos(a))^2

 Exercise

$cos^2a+\left(cot\:a\:\cdot\:cos\:a\right)^2$

 

The power of a product is equal to the product of it's factors raised to the same power

$\cos\left(a\right)^2+\cot\left(a\right)^2\cos\left(a\right)^2$

 

Factor the polynomial $\cos\left(a\right)^2+\cot\left(a\right)^2\cos\left(a\right)^2$ by it's greatest common factor (GCF): $\cos\left(a\right)^2$

$\cos\left(a\right)^2\left(1+\cot\left(a\right)^2\right)$

 

Apply the trigonometric identity: $1+\cot\left(\theta \right)^2$$=\csc\left(\theta \right)^2$, where $x=a$

$\cos\left(a\right)^2\csc\left(a\right)^2$

 Why is cot(x)^2+1 = csc(x)^2 ?

$\cos\left(a\right)^2\csc\left(a\right)^2$

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