Question

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

Answer 1

SOLUTION

(3) We want to prove the trig identity

$\frac{sin(x)+sin(x).cot^2(x)}{csc(x)}=1$

This becomes

$\begin{gathered} \frac{sin(x)+sin(x).cot^2(x)}{csc(x)}=1 \\ \frac{sin(x)+(sin(x)\times\frac{1}{tan^2(x)})}{\frac{1}{sin(x)}} \\ \frac{sin(x)+(sin(x)\times\frac{cos^2(x)}{sin^2(x)})}{\frac{1}{sin(x)}} \\ \frac{sin(x)+\frac{cos^2(x)}{sin(x)}}{\frac{1}{sin(x)}} \end{gathered}$

Changing the division to multiplication for thedenominator, we have

$\begin{gathered} (sin(x)+\frac{cos^2(x)}{sin(x)})\times sin(x) \\ =sin^2(x)+cos^2(x) \\ =1 \end{gathered}$