What is the general solution for sin(x)cos(2x)-cos(x)sin(2x)=(sqrt(3))/2 ?

The general solution for sin(x)cos(2x)-cos(x)sin(2x)=(sqrt(3))/2 is x=-pi/3-2pin,x=-(2pi)/3-2pin

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

sin (x) cos (2 x) - cos (x) sin (2 x) = \frac{3}{2}

x = - \frac{π}{3} - 2 πn, x = - \frac{2 π}{3} - 2 πn

Solution steps

sin (x) cos (2 x) - cos (x) sin (2 x) = \frac{3}{2}

Rewrite using trig identities

sin (x - 2 x) = \frac{3}{2}

General solutions for

sin (x - 2 x) = \frac{3}{2}

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

Solve

x - 2 x = \frac{π}{3} + 2 πn : x = - \frac{π}{3} - 2 πn

Solve

x - 2 x = \frac{2 π}{3} + 2 πn : x = - \frac{2 π}{3} - 2 πn

x = - \frac{π}{3} - 2 πn, x = - \frac{2 π}{3} - 2 πn

5 sin^{2} (x) + 3 sin (x) = 1

8 cos^{2} (x) - 16 cos (x) + 8 = 0

\frac{2}{3} = sin (x)

cos (2 θ) + 10 sin^{2} (θ) = 3

- 2 sin (3 θ) = 1

What is the general solution for sin(x)cos(2x)-cos(x)sin(2x)=(sqrt(3))/2 ?
The general solution for sin(x)cos(2x)-cos(x)sin(2x)=(sqrt(3))/2 is x=-pi/3-2pin,x=-(2pi)/3-2pin