Question

I need help with proving the identity csc(x) - cos(x) cot(x) = sin(x)? Will give medal & fan.

All I need for this is the reasoning. I have the proof step-by-step, but I need the reasons for these steps. I'll be posting the steps in the comments.

Answer 1

Step 1

csc(x) - cos(x) cot(x) = (1/sin(x)) - cos(x)(cos(x)/sin(x))

Answer 2

Cosec(x)=1/Sinx and Cotx=Cosx/Sinx

Answer 3

Step 2

csc(x) - cos(x) cot(x) = (1/sin(x)) - (cos^2 (x) / sin(x))

Answer 4

cosx*cosx=cos^2(x)

Answer 5

Step 3

csc(x) - cos(x) cot(x) = (1 - cos^2 (x)) / sin(x)

Answer 6

Lcm on both side.