first one 2x+3x = 90, or pi/2. and same angle in the third quarter with the 2n pi
the seond one use the identity
tan^2 x + 1 = sec ^2 x
1.
Write to get the polynomial .
It's easy to see that satisfies this equation, so is a factor, and long division gives
So you need to solve (easy), as well as and (not so easy). All will have exact value answers though. This will help you.
√3 tanx-secx-1=0
√3 sinx/cosx -1/cosx -1=0
√3 sinx-1- cosx=0
√3/2 sinx-1/2 cosx=1/2 {2 is √((√3)^2+(-1)^2 )}
cos〖π/6 sinx-〗 sin〖π/6〗 cosx=sin〖π/6〗
sin〖(π/6-x)=〗 sin〖π/6〗
π/6-x=nπ+(-1)^n π/6
x=π/6-nπ-(-1)^n π/6
here n is a integer