Question

angle difference identity to find the exact value of ;
cos 2 θ = cos θ + 2 for 0 < θ < 2p

Answer 1

\[\cos 2 \theta\]or \[\cos ^{2}\theta \]

Answer 2

Is that an equation?

Way 1: Since \(\cos \theta \in [-1,1]\), the only way that this equation has a solution is \(\cos2\theta = 1\) and \(\cos\theta = -1\).

Way 2: \(\cos(2\theta) = 2\cos^2\theta - 1\) which turns out to be a quadratic.

Way 3: the one suggested by your question. \(\cos(2\theta) -\cos(\theta) = 2\). Now \(\cos C - \cos D = 2\sin \left(\frac{C + D}{2}\right)\sin\left(\frac{D - C}{2}\right)\). Use this identity.