Question

Verify Cos(x)[sec(x)-Cos(x)]=Sin(x)

Answer 1

(cosx/cosx) - cos^2(x) = sinx
1 - cos^2(x) = sinx
cos^2(x) =1 - sin^2(x)
sin^2(x) =sin(x)
Nope.

Answer 2

It works if the equation should be Cos(x)[sec(x)-Cos(x)]=Sin^2(x)
If it's just a normal Sin(x), it doesn't work.

Cos(x) x Sec(x) is 1
Cos(x) x -Cos(x) is -Cos^2(x)
so
1 - Cos^2(x) = Sin^2(x)

Pythagorean Identity: sin^2(x) + cos^2(x) = 1
Subtract cos
so 1 - Cos^2(x) = Sin^2(x)
therefore
Sin^2(x) = Sin^2(x)