Originally Posted by

**Archie Meade** $\displaystyle \frac{3z}{2}+75^o=210^o,\ 330^o,\ 570^o,\ 690^o....$

$\displaystyle \frac{3z}{2}=135^o,\ 255^o,\ 495^o,\ 615^o....$

$\displaystyle 3z=270^o,\ 510^o,\ 990^o,\ 1230^o....$

$\displaystyle z=90^o,\ 170^o,\ 330^o.......$

(2) $\displaystyle 2tan2x+sec40^o=1$

$\displaystyle 2tan2x+\frac{1}{cos40^o}=1$

$\displaystyle 2tan2x=1-\frac{1}{cos40^o}$

$\displaystyle tan2x=\frac{cos40^o-1}{2cos40^0}$

That can be evaluated and you can finish with the identity $\displaystyle tan2x=\frac{2tanx}{1-tan^2x}$

to get a quadratic equation in tanx.