SOLUTION: Please help me solve this problem! If cosx = 1/5. Find all possible values of secx - tanx/ sinx. Now, the answer at the back of the book is: {{{(25sqrt(6) - 60)/12}}} ; {{{(-

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me solve this problem! If cosx = 1/5. Find all possible values of secx - tanx/ sinx. Now, the answer at the back of the book is: {{{(25sqrt(6) - 60)/12}}} ; {{{(-      Log On


   

Question 1052209: Please help me solve this problem!
If cosx = 1/5. Find all possible values of secx - tanx/ sinx.
Now, the answer at the back of the book is: %2825sqrt%286%29+-+60%29%2F12 ; %28-25sqrt%286%29+-+60%29%2F12
I just can't quite get there. I know you have to turn everything into cos, because that is what you have a value for.
So I got: 1/cosx - sinx/cosx for the numerator. You can add these because the denominators are the same. So it would be: 1 - sinx/cosx. And all of this over sinx.
Then I thought, hmmmm, what if I were to multiply the numerator and denominator by sinx. That would give me: sinx - sin^2x / cosx / sin^2x. And sin^2x = 1 - cos^2x, so that takes care of that, but I still have that sinx at the beginning that I can't get rid of. :(
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve this problem!
If cosx = 1%2F5, Find all possible values of %28secx+-+tanx%29%2F+%28sinx%29

This is long but bear with me.
if cos%28x%29=1%2F5 then
cos%5E2%28x%29+sin%5E2%28x%29=1
%281%2F5%29%5E2+sin%5E2%28x%29=1
%281%2F25%29+sin%5E2%28x%29=1
sin%5E2%28x%29=1-%281%2F25%29
sin%5E2%28x%29=25%2F25-%281%2F25%29
thus
sin%28x%29=sqrt%2824%2F25%29 or sin%28x%29=-sqrt%2824%2F25%29
remember that
sqrt%2824%2F25%29=%282%2Asqrt%286%29%29%2F%285%29

%28secx+-+tanx%29%2F+%28sinx%29

%28%281%2Fcos%28x%29%29+-+%28sin%28x%29%29%2F%28cos%28x%29%29%29*%281%2F%28sin%28x%29%29%29

%28%281-sinx%29%2Fcos%28x%29%29*%281%2F%28sin%28x%29%29%29


%28%281-sqrt%2824%2F25%29%29%2F%281%2F5%29%29*%281%2F%28sqrt%2824%2F25%29%29%29
5*%28%281-sqrt%2824%2F25%29%29%29*%281%2F%28sqrt%2824%2F25%29%29%29
simplify to get
%282%2Asqrt%286%29%2A25-24%2A5%29%2F%2824%29
%282%2Asqrt%286%29%2A25-120%29%2F%2824%29
%28sqrt%286%29%2A25-60%29%2F%2812%29