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

The general solution for 3tan(2x-pi/2)=2sin(pi/3) is x=(pin)/2+pi/3

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3tan(2x-pi/2)=2sin(pi/3)

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

x = \frac{πn}{2} + \frac{π}{3}

Solution steps

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

sin (\frac{π}{3}) = \frac{3}{2}

3 tan (2 x - \frac{π}{2}) = 2 \cdot \frac{3}{2}

Multiply fractions:

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

3 tan (2 x - \frac{π}{2}) = \frac{3 \cdot 2}{2}

Cancel the common factor:

2

3 tan (2 x - \frac{π}{2}) = 3

Divide both sides by

3

tan (2 x - \frac{π}{2}) = \frac{3}{3}

General solutions for

tan (2 x - \frac{π}{2}) = \frac{3}{3}

2 x - \frac{π}{2} = \frac{π}{6} + πn

Solve

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

x = \frac{πn}{2} + \frac{π}{3}

2 tan (x) - 2 = 0, 0 \leq x \leq 2 π

tan (3 5^{\circ}) tan (5 6^{\circ} - x) = 1

42.25 = 0.1681 cos (b)

\frac{tan ( 3 x )}{tan ( 2 x )} = 1

6 cot (x) = 5 - tan (x)

What is the general solution for 3tan(2x-pi/2)=2sin(pi/3) ?
The general solution for 3tan(2x-pi/2)=2sin(pi/3) is x=(pin)/2+pi/3