solution set 9sec^2xtanx=12tanx

[btrfly24]

I'm completely lost and I don't understand what my book is talking about. I don't even know where to start. Please help!!

solution set 9sec^2xtanx=12tanx

 

[arthur ohlsten]

9 sec^2x tanx = 12 tan x rewrite
9 sec^2xtanx - 12 tanx=0 factor out 3 tanx
3 tanx [ 3 sec^2x-4]=0
3 tan x=0 OR 3sec^2x-4=0
but 3 can't =0
tanx=0 answer Or
3 sec^2x-4=0
3sec^2x=4
sec^2x=4/3 but I like to work with sin and cos, so:
cos^2x=3/4
cosx=+/- 1/2 sqrt3 answer

Arthur
you can convert to angles if your instructor requires angular answers

 

[btrfly24]

thanks so much arthur. Factoring out that three makes all the difference!