sqrt(3)cos(2x)=2sin(x)cos(2x)

Solution

3 cos (2 x) = 2 sin (x) cos (2 x)

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Solution steps

3 cos (2 x) = 2 sin (x) cos (2 x)

Subtract

2 sin (x) cos (2 x)

from both sides

3 cos (2 x) - 2 sin (x) cos (2 x) = 0

Factor

3 cos (2 x) - 2 sin (x) cos (2 x) : cos (2 x) (3 - 2 sin (x))

cos (2 x) (3 - 2 sin (x)) = 0

Solving each part separately

cos (2 x) = 0 or 3 - 2 sin (x) = 0

cos (2 x) = 0 : x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

3 - 2 sin (x) = 0 : x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

3 tan (θ) - 2 sin (θ) tan (θ) = 0

\frac{sin ( 2 x )}{sin ( x )} = 1.5

x, yz = sin (x y)

sin^{2} (x) = \frac{( 5 m - 5 )}{2}

2 cot (2 x) = 4