If sinx×secx=-1 then find sinx and secx?

Trigonometry is based on a picture of a circle with the radius making an angle with the x axis. You carry this picture in your head, not your calculator. Trig is mostly imagination and the rest memorization.

Remember Chief SohCahToa
Sin = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent

Also memorize:
Sec = 1/Cos
Csc = 1/Sin
Cot = 1/Tan

Given sin(x) × sec(x) = -1 one value is +1 and the other is -1. That happens at x=-π/4.

www.wolframalpha.com/input/?i=plot+y%3Dsin(x)+%C3%97+sec(x)
www.wolframalpha.com/input/?i=solve+sin(x)+%C3%97+sec(x)%3D-1