Question

Find cos(20) if 0=pi/3

Answer 1

`\bf \textit{Double Angle Identities} \\ \quad \\ cos(2\theta)= \begin{cases} cos^2(\theta)-sin^2(\theta)\\ 1-2sin^2(\theta)\\ \boxed{2cos^2(\theta)-1} \end{cases}\\\\ -------------------------------\\\\ cos(2\theta)\implies 2cos^2(\theta)-1\qquad \theta=(\pi )/(3)\implies 2\left[ cos\left( (\pi )/(3) \right)\right]^2-1 \\\\\\ 2\left[ \cfrac{1}{2} \right]^2-1\implies 2\cdot \cfrac{1}{4}-1\implies \cfrac{1}{2}-1\implies -\cfrac{1}{2}`