six/siny=1/2 and cosx/cosy=3 prove: cos (x+y)=(7 cos^2 x -6)/3?

Answer 1

cos(x+y) = cos(x)cos(y) - sin(x)sin(y)

Solve sin(x)/sin(y)=1/2 for sin(y) in terms of sin(x);
solve cos(x)/cos(y)=3 for cos(y) in terms of cos(x);
put these into the identity above.

Lastly, you will need the fact that sin²(x) = 1 - cos²(x)