The number of solutions of sin3x = cos 2x, in the interval \[\left( {{\pi \over 2},\pi } \right)\] is :
Solutions · 1
Official solution
sin 3x = cos 2x
\[ \Rightarrow \] 3 sin x−4 sin3 x = 1−2 sin2 x⇒\[\,\,\,\] 4 sin3 x - 2 sin2 x - 3 sin x + 1 = 0
\[ \Rightarrow \] sin x = 1,8−2±25In the interval\left( {{\pi \over 2},\pi } \right) (, sin x = \]{{ - 2 + 2\sqrt 5 } \over 8}