Question

cotx = -2 and 0 less than or equal to x less than or equal to pi

Find sin2x and cos2x

How to get the answers of sin2x = -4/5, cos2x = 3/5?

Answer 1

If cot x = -2 and x is in the first or second quadrant, it must be in the second quadrant, with a horizontal (x') coordinate -2 times the vertical (y') coordinate. The cosine of x is 2/sqrt 5 and the sine is -1/sqrt 5. You get that from the Pythagorean theorem and the fact that you are in the second quadrant.

Sin 2x = 2 sin x cos x = 2*(-2)/5 = -4/5
Cos 2x = cos^2 x - sin^2 x = 4/5 - 1/5 = 3/5