Given csc x/cot x = Square root of 2, find a numerical value of one trigonometric function of x.

cscx/cotx = 1/sin (x) / (cos (x) / sin (x)) = 1*sin (x) / (sin (x) * cos (x)) = 1/cos (x) = sqrt (2)

Now solve for x

1/cos (x) = sqrt (2)

cos (x) = 1/sqrt (2) = sqrt (2) / 2

=> x=2k π ± π / 4 (general solution)

Thus for x in the first quadrant, x=45 degrees, and

sin (x) = sqrt (2) / 2 = 0.70710678

cos (x) = sqrt (2) / 2 = 0.70710678

tan (x) = sin (x) / cos (x) = 1