Question

Solve for exactly: cos(2a)= -sin a with 0≤a≤2π

Answer 1

Couple identities that will help\[cos(2\alpha)=cos^{2}\alpha - sin^{2}\alpha\]\[cos^{2}\alpha=1-sin^{2}\alpha\]
Convert your left side using these and you'll get a quadratic equation. Solve for sin(a) then solve for a.