Question

$sec^{2}x$·$cotx-cotx = tanx$

I'm supposed to prove this but don't know how? Can someone help, please!

Answer 1

sec²(x)cot(x) - cot(x) = (1/cos²(x))(cos(x)/sin(x)) - cos(x)/sin(x)
= (1/cos(x))(1/sin(x)) - cos(x)/sin(x)
= (1/cos(x))(1/sin(x)) - cos²(x)/( cos(x)sin(x))
= (1-cos²(x))/(cos(x)sin(x))
= sin²(x)/(cos(x)sin(x))
= sin(x)/cos(x)
= tan(x)