Solve the equation sin2x cos xSolution sin 2x cos x spli

Solve the equation | sin(2x)| = cos x.

| sin (2x) | = cos x

splitting the absolute value into two parts

sin (2x) = cos x or sin (2x) = -cos x

sin (2x ) = cos x

2 sin x cos x - cos x = 0

cos x ( 2 sin x - 1 ) = 0

cos x = 0

sin x = 1/2

x = pi/2 + 2npi , 3pi/2 + 2npi , pi/6 + 2npi , 5pi/6 + 2npi

solving the 2nd part

sin (2x) = -cos x

2 sin x cos x + cos x = 0

cos x ( 2 sin x + 1 ) = 0

cos x = 0

sin x = -1/2

x = 7pi/6 + 2 npi , 3pi/2 + 2npi , 11pi/6 + 2npi , pi/2 + 2npi

solutions are

pi/2 + 2npi or 3pi/2 + 2npi or pi/6 + 2npi or 5pi/6 + 2npi or 7pi/6 + 2 npi or 11pi/6 + 2npi