How to solve this one, Thank you

Question

If , where x in quadrant III, then find the exact value of each of the following. Give your answer as a reduced fraction.

sin   

   

Answer 1

Note that 20-99-101 is a Pythagorean triple. Since we are in the third quadrant, sin x = -20/101 and cos x = -99/101

a) sin(2x) = 2 sin(x)cos(x) = 2 (-20/101)(-99/101) = 3960/10201

b) cos(2x) = cos^2(x) - sin^2(x) = (-99/101)^2 - (-20/101)^2 = 9401/10201

c) tan(2x) = 2 tan(x)/(1 - tan^2(x)) = 2 * 20/99/(1 - (20/99)^2) = 3960/9401