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

Question

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

anonymous · Answer

$$\cos 2 \theta$$or $$\cos ^{2}\theta $$

parthkohli · Answer

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.