cotx=1 how do you find cos2x?

cot(x) = 1 = cos(x)/sin(x) therefore, move sin(x) to the other side, that means sin(x) = cos(x) for the angle you want.

You know your angle is between -90 and -180, so based on the unit circle, what angle must this be? It lives in the third quadrant, and you know sin(x)=cos(x); conclusion, -135 degrees.

Now you want to know what cos(2*-135) is, well that is the same as cos(-270). So start at 0 (horizontal positive x axis), and move around the unit circle 270 degrees clockwise (negative direction). You end up at 90 degrees. what is the cos(90) = cos(-270); conclusion, 0.

You can do this using trig identities please let x= A

CotA = CosA/SinA so all we have to do is find where on the unit circle between -180 and -90 the Cotangent value is 1.

This occurs at -135 degrees where the value of the x coordinate is the square root of 2 over 2 and the y value is the same.

Now we need to use the double angle formula for cos to find what cos2A equals

cos2a=cos^2(a)-sin^2(a)

so you plug in -135 for A and do the math on a calculator or however you choose

so cos2A = 0

If my math is correct, however, I would check the last step of computations if I were you!