SOS! math problems...btw I need the answers fast?

Question

1) cos2X - cosX -2=0 , X=?


2) sin9X+ sin10X+ sin11X=0 , X=?

3) cos8X.cos10X=1/2 cos18X , X=?

Answer 1

1) expand cos2x to get 2cos^2x -1 -cosx - 2 = 0
rearrange to 2cos^2x-cosx-3 = 0. Let y = cosx, the eq becomes a quadratic 2y^2 - y - 3 = 0; solve for y. Then x = arccos(y).

2) Write this like sin(10x - x) + sin(10x) + sin(10x + x) = 0
Use the sin(a-b) = sin(a)cos(b)-cos(a)sin(b) and sin(a+b) = sin(a)cos(b)+cos(a)sin(b) where a = 10x and b = x

3) Let cos(8x) = cos(9x-x), cos(10x) = cos(9x+x) and cos(18x) = cos(2*9x). Again use the double angle and sum and difference angle identities to get all cos and sin terms with the same arguments.