I am supposed to prove that for all real numbers $\displaystyle a,b, \theta$ that

$\displaystyle (acos\theta+bsin\theta)^2\leq a^2+b^2$

I've only gotten up to this point which is where I am not sure as to how to appply the cauchy schwarz inequality,

$\displaystyle (acos\theta+bsin\theta)^2=a^2+b^2-(asin\theta+bcos\theta)^2$

Am I on the right track?