can any1 help?

Question

f(x)=csc(x)+sec(x), 0
find the points at which the tangent line is horizontal

Answer 1

cosec=1/sin and sec =1/cos
so 1/sin x +1/cos x = f(x)
f´(x) = -cosx/sin^2+ sin x/cos^2x = (sin^3x-cos^3x)/sin^2x*cos^2x
sin^3x-cos^3x= (sin x-cos x) (sin^2x+sinx*cosx +cos^2x)=0
so sin x -cos x = 0 x=pi/4
sinx cosx+1 = 0
so 1/2 sin 2x = -1 and sin 2x =-2 impossible so the solution is x =pi/4