What is the general solution for 4sin(x)cos(x)=-sqrt(3) ?

The general solution for 4sin(x)cos(x)=-sqrt(3) is x=(2pi)/3+pin,x=(5pi)/6+pin

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4sin(x)cos(x)=-sqrt(3)

4 sin (x) cos (x) = - 3

x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

Solution steps

4 sin (x) cos (x) = - 3

Rewrite using trig identities

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

\frac{sin ( 2 x ) \cdot 4}{2} = - 3

Divide the numbers:

\frac{4}{2} = 2

2 sin (2 x) = - 3

Divide both sides by

2

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

General solutions for

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

2 x = \frac{4 π}{3} + 2 πn, 2 x = \frac{5 π}{3} + 2 πn

Solve

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

Solve

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

x = \frac{2 π}{3} + πn, x = \frac{5 π}{6} + πn

t, x = 3 cos (t)

tan^{2} (θ) = - \frac{3}{2} sec (θ), 0 \leq θ < 2 π

5 sin (x) + 3 cos (x) = 0

3 cos (x) csc (x) = 2 cos (x)

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

What is the general solution for 4sin(x)cos(x)=-sqrt(3) ?
The general solution for 4sin(x)cos(x)=-sqrt(3) is x=(2pi)/3+pin,x=(5pi)/6+pin