Find a numerical value of one trigonometric function of x if

Question

tanx/cotx - secx/cosx = 2/cscx

a) cscx=1
b) sinx=-1/2
c)cscx=-1
d)sinx=1/2

Answer 1

(sinx/cosx)/(cosx/sinx) - (1/cosx)/cosx = 2sinx
(sin^2 x)/(cos^2 x) - 1/cos^2 x = 2sinx
(sin^2 x - 1)/cos^2 x = 2sinx
(sin^2 x - 1)/(1 - sin^2 x) = 2sinx
-1 = 2sinx
sinx = -1/2