Prove the trigonometric identity sin(w)(1+cot(w)^2)=csc(w)

 Exercise

$\left(\sin\left(w\right)\right)\left(1+\cot^2\left(w\right)\right)=\csc\left(w\right)$

 

Starting from the left-hand side (LHS) of the identity

$\sin\left(w\right)\left(1+\cot\left(w\right)^2\right)$

 

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

$\sin\left(w\right)\csc\left(w\right)^2$

 Why is cot(x)^2+1 = csc(x)^2 ?

 

Since $\sin$ and $\csc$ are opposite functions they cancel when multiplying

$\csc\left(w\right)^{1}$

 

Any expression to the power of $1$ is equal to that same expression

$\csc\left(w\right)$

 

Since we have reached the expression of our goal, we have proven the identity

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