The value of the limit limx → π/2 (4√2(sin 3x + sin x)/(2 sin 2x sin 3x/2 + cos 5x/2) - (√2 + √2 cos 2x + cos 3x/2))

Question

The value of the limit

\( \lim\limits_{x \to \frac{\pi}{2}}\frac{4\sqrt{2}(sin3x\,+\,sinx)}{(2sin2xsin\frac{3x}{2}\,+\,cos\frac{5x}{2})\,-\,(\sqrt2\,+\,\sqrt2cos2x\,+\,cos\frac{3x}{2})}\) is ___

Answer 1

\( \lim\limits_{x \to \frac{\pi}{2}}\frac{16\sqrt{2}sinx}{8sinx.sin\frac{x}{2}\,-\,2\sqrt2}\) = 8