Question

Solve the equation in the interval [0, 2pi). tan(x/2)=-1

Answer 1

tan is negative in 2nd and 4th quadrant. tan\[\tan \frac{ 3\pi }{ 4 }=-1\] and
\[\tan \frac{ 7\pi }{ 4 }= -1\]
hence 3pi/4=x/2 and 7pi/4 = x/2.
i.e x=3pi/2 and x=7pi/2