prove the following trigonometric identity

Question

(sin²∅-1)/tan²∅-1=(1/sin²∅)-1

Answer 1

pick an angle & plug it into the equation

let the angle = pi/6, sin(pi/6) = 1/2

tan(pi/6) = 1/sqr3

sin^2(pi/4) = 1/4, tan^2(pi/4) = 1/3

(1/4 - 1)/(1/3-1) = (1/(1/4-1)) -1

-3/4)/(-2/3) = -4/3 -1

-3/4 x -3/2 = -7/3

-9/8 doesn't equal -7/3

one counterexample disproves the "identity"