What is the general solution for tan((3x)/2+pi/2)=1 ?

The general solution for tan((3x)/2+pi/2)=1 is x=(2pin)/3-pi/6

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tan((3x)/2+pi/2)=1

tan (\frac{3 x}{2} + \frac{π}{2}) = 1

x = \frac{2 πn}{3} - \frac{π}{6}

Solution steps

tan (\frac{3 x}{2} + \frac{π}{2}) = 1

General solutions for

tan (\frac{3 x}{2} + \frac{π}{2}) = 1

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

Solve

\frac{3 x}{2} + \frac{π}{2} = \frac{π}{4} + πn : x = \frac{2 πn}{3} - \frac{π}{6}

x = \frac{2 πn}{3} - \frac{π}{6}

2 tan^{2} (x) + sec^{2} (x) = 2

3 sin (x) + 4 cos (x) = 5

4 cos (2 t) + 1 = 3, 0 \leq t \leq \frac{π}{2}

4 cos^{3} (x) = 3 cos (x)

7 cos (2 t) = 3

What is the general solution for tan((3x)/2+pi/2)=1 ?
The general solution for tan((3x)/2+pi/2)=1 is x=(2pin)/3-pi/6