Question

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

Answer 1

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