For what values of theta in 0 2pi we have tan theta squarer

For what values of theta in [0, 2pi] we have tan theta = squareroot sec^2 theta - 1? Make sure you justify your answer.

Solution

tan theta=sqrt(sec²theta -1)

here tan theta is positive

and tan theta is positive in first and third quadrant

therefore the answer is [0,pi/2)U[pi,3pi/2)