Question

solve for x: sec(x) * cos ((pi/2) - x) = -1

Answer 1

Domain is [0,2pi)

Answer 2

There exists a trig identity such that you can say:
cos((pi/2)-x) = cos(pi/2)cos(x) + sin(pi/2)sin(x)

cos(pi/2) = 0
sin(pi/2) = 1

So now our equation ends up being
sec(x)*(0*cos(x) + sin(x)) = -1

that simplifies to:
sec(x)*sin(x) = -1

That should be enough for you to figure out the rest. Lemme know if you need anymore help.

Answer 3

\[\cos (\frac{\pi}{2}-x)=\sin x\]