how do you find the solutions to $$\cos 2\theta-\sin \theta=1$$?

Question

jamesj · Answer

Remember that
cos 2x = cos^2 x - sin^2 x
           = 1 - 2 sin^2 x

Hence your equation can be written as a quadratic equation in sin

anonymous · Answer

ok so i get 2sin^2theta+sintheta-2. how do i solve to find solutions from here?

jamesj · Answer

Write, for instance, x = sin theta.  Then you have a quadratic in x.  Solve that quadratic in x.  And then find theta such that sin theta = x.

anonymous · Answer

ok thank you

anonymous · Answer

hello again, do you know how to prove the equation, $$(\sin 3\theta \div \sin \theta)-(\cos3\theta \div \cos \theta)=2$$, is an idenity?