Question

“Find the trig identity” I’m in need of help on number 3

Answer 1

(3) We want to prove the trig identity

`(sin(x)+sin(x).cot^2(x))/(csc(x))=1`

This becomes

`\begin{gathered} (sin(x)+sin(x).cot^2(x))/(csc(x))=1 \\ (sin(x)+(sin(x)*(1)/(tan^2(x))))/((1)/(sin(x))) \\ (sin(x)+(sin(x)*(cos^2(x))/(sin^2(x))))/((1)/(sin(x))) \\ (sin(x)+(cos^2(x))/(sin(x)))/((1)/(sin(x))) \end{gathered}`

Changing the division to multiplication for thedenominator, we have

`\begin{gathered} (sin(x)+(cos^2(x))/(sin(x)))* sin(x) \\ =sin^2(x)+cos^2(x) \\ =1 \end{gathered}`