Question 733434
<pre>
      6·tan&#952; + secē&#952; = 8

Use the identity: secē&#952; = 1 + tanē&#952;

  6·tan&#952; + 1 + tanē&#952; = 8

Get 0 on the right side and arrange in 
descending order:

   tanē + 6·tan&#952; - 7 = 0

That factors as:

(tan&#952; + 7)(tan&#952; - 1) = 0

tan&#952; + 7 = 0        tan&#952; - 1 = 0
    tan&#952; = -7           tan&#952; = 1

Maybe you can finish from here.  You didn't say whether you 
wanted the solutions in radians or degrees and whether you 
wanted only the solutions in the interval [0,360°), [0,2<font face="symbol">p</font>)
or whether you wanted all infinitely many solutions by writing 
an expression in terms of integer n.

Edwin</pre>