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

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

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

4 sin (x) cos (x) = 3

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

Solve

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

Solve

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

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

3 sin (x) + 4 cos (x) = 2

cot^{2} (x) - 6 cot (x) + 5 = 0, 0 \leq x \leq 2 π

9 tan (θ) + 13 = 2 tan (θ) + 6

2 = 3 sin (∣ 5 x ∣) + 1

sin (θ) = - \frac{1}{3}

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