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

The general solution for tan(x/2-pi/2)=sqrt(2) is x=2*0.95531…+2pin+pi

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tan(x/2-pi/2)=sqrt(2)

tan (\frac{x}{2} - \frac{π}{2}) = 2

x = 2 \cdot 0.95531 \dots + 2 πn + π

Solution steps

tan (\frac{x}{2} - \frac{π}{2}) = 2

Apply trig inverse properties

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn

Solve

\frac{x}{2} - \frac{π}{2} = arctan (2) + πn : x = 2 arctan (2) + 2 πn + π

x = 2 arctan (2) + 2 πn + π

Show solutions in decimal form

x = 2 \cdot 0.95531 \dots + 2 πn + π

8 sec (x) + 8 tan (x) = 8

25 cot^{2} (θ) - 16 = 0

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

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

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

What is the general solution for tan(x/2-pi/2)=sqrt(2) ?
The general solution for tan(x/2-pi/2)=sqrt(2) is x=2*0.95531…+2pin+pi