Question

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

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

ok thank you

Answer 5

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?