Determine the value of the specific trigonometric function a

Determine the value of the specific trigonometric function.

a) If cos x = -5/13 and P(x) is in quadrant III, find sin 2x.

b) If cot = 3/4 and is in quadrant IV, find cot 2.

Verify the identity.

c) tan 2y=2 cot y/csc² y-2 (as a fraction, not division)

d) sin 2=2tan/1+tan² (as a fraction, not division)

a. cos x=-5/14

here adjacent =5 and hypotenuse=-13

therefore sin x=-12/13

sin2x=2sinxcosx=2* -12/13 *-5/13= 60/13

b. cot 2x= 1/2(cot x - tan x)

cot x= 3/4 therefore tan x=4/3

cot 2x=1/2(3/4 - 4/3)=1/2(25/12)=25/24