Step-by-step explanation:
sin(x)×csc(x) - cos²(x) = sin²(x)
csc(x) = 1/sin(x) (basic definition)
therefore,
sin(x)×csc(x) = sin(x) × 1/sin(x) = 1
1 - cos²(x) = sin²(x)
1 = sin²(x) + cos²(x)
and that is again a basic definition based on the standard circle with radius = 1. there we have the Pythagoras principle, as sin and cos are the legs of a right-angled triangle, with radius 1 being the Hypotenuse.
