sec*2 (x) = 2 tan^2 (x) Note that tan 2(x) + 1 = sec 2 (x)....so we can write tan 2(x) + 1 = 2tan*2(x) rearrange as tan*2(x) =1 subtract 1 from both sides tan 2 (x) - 1 = 0 factor (tan (x) + 1) ( tan (x) - 1) = 0 Set each factor to ) and solve tan (x) + 1 = 0 tan (x) - 1 = 0 tan (X) = -1 tan (X) = 1 And this is true at And this is true at 3pi/4 + n*pi pi/4 + n*pi