Question

Solve: 2√(3) cos²A= sinA​

Answer 1

Explanation:

`2√(3)\cos ^2\left(A\right)=\sin \left(A\right)\\\mathrm{Subtract\:}\sin \left(A\right)\mathrm{\:from\:both\:sides}\\2√(3)\cos ^2\left(A\right)-\sin \left(A\right)=0\\-\sin \left(A\right)+\left(1-\sin ^2\left(A\right)\right)\cdot \:2√(3)=0\\\sin \left(A\right)=-(2√(3))/(3),\:\sin \left(A\right)=(√(3))/(2)\\\mathrm{Combine\:all\:the\:solutions}\\A=(\pi )/(3)+2\pi n,\:A=(2\pi )/(3)+2\pi n4`