Question 1052209
Please help me solve this problem!

If {{{cosx}}} = {{{1/5}}}, Find all possible values of {{{(secx - tanx)/ (sinx)}}}


This is long but bear with me.

if {{{cos(x)}}}={{{1/5}}} then

{{{cos^2(x)}}}+{{{sin^2(x)}}}={{{1}}}

{{{(1/5)^2}}}+{{{sin^2(x)}}}={{{1}}}
{{{(1/25)}}}+{{{sin^2(x)}}}={{{1}}}

{{{sin^2(x)}}}={{{1}}}-{{{(1/25)}}}

{{{sin^2(x)}}}={{{25/25}}}-{{{(1/25)}}}

thus 

{{{sin(x)}}}={{{sqrt(24/25)}}} or {{{sin(x)}}}=-{{{sqrt(24/25)}}} 

remember that

{{{sqrt(24/25)}}}={{{(2*sqrt(6))/(5)}}} 


{{{(secx - tanx)/ (sinx)}}}


{{{((1/cos(x)) - (sin(x))/(cos(x)))}}}*{{{(1/(sin(x)))}}}


{{{((1-sinx)/cos(x))}}}*{{{(1/(sin(x)))}}}



{{{((1-sqrt(24/25))/(1/5))}}}*{{{(1/(sqrt(24/25)))}}}

{{{5}}}*{{{((1-sqrt(24/25)))}}}*{{{(1/(sqrt(24/25)))}}}

simplify to get

{{{(2*sqrt(6)*25-24*5)/(24)}}}

{{{(2*sqrt(6)*25-120)/(24)}}}

{{{(sqrt(6)*25-60)/(12)}}}