Question

Find all solutions for the following equations. Write your answers in radians using exact values. (Enter your answers as a comma-separated list. Let k be any integer.) sin 2x cos x cos 2x sin x

Answer 1

Answer:

Step-by-step explanation:

Given that:

sin2xcos x + cos2xsin x = -1

Recall that;

SInAcosB + cosASinB = SIn (A+B)

SIn (2x +x) = -1

Sin (3x) = -1

$x = \bigg [\dfrac{Sin ^{-1} (-1)}{3} \bigg ]$

$x = \dfrac{\pi}{2} + \dfrac{2 \pi \ k}{3}$

$x = \dfrac{\pi}{2}, \dfrac{7 \pi}{6}, \dfrac{11 \pi}{6}$