​ Prove that (2√3 + 3)sin x + 2√3 cos x lies between -(2√3 +√15 ) and (2√3 +√15 ). ​

Question

Prove that \((2\sqrt3+3)\)sin x + \(2\sqrt2\) cos x lies between - \((2\sqrt3+\sqrt{15})\)and \((2\sqrt3+\sqrt{15})\).

Answer 1

Let f(x) =(2√3 + 3) sin x + 2√3 cos x 

Here A = 2√3 , B = 2√3 + 3 And c = 0

Hence proved.