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

Explanation:

Given that:

sin2xcos x + cos2xsin x = -1

Recall that;

SInAcosB + cosASinB = SIn (A+B)

SIn (2x +x) = -1

Sin (3x) = -1

`x = \bigg [(Sin ^(-1) (-1))/(3) \bigg ]`

`x = (\pi)/(2) + (2 \pi \ k)/(3)`

`x = (\pi)/(2), (7 \pi)/(6), (11 \pi)/(6)`