SOLUTION: Prove the identity: {{{cos(x)/(1-sin(x)) + cos(x)/(1+sin(x)) = 2*((1+tan^2(x))/sec(x))}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Prove the identity: {{{cos(x)/(1-sin(x)) + cos(x)/(1+sin(x)) = 2*((1+tan^2(x))/sec(x))}}}      Log On


   

Question 976209: Prove the identity:
Found 2 solutions by DAWNPLAYA, Boreal:
Answer by DAWNPLAYA(3) About Me  (Show Source):
You can put this solution on YOUR website!
Answer part 1: . Add me on Skype I'll send you the other 2 parts. This is an app called Symbolab that can do almost anything in math. My skype is DAWNPLAYA55. Don't be surprised tha I'm so young :)

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
term on left over (1-sinx^2)
{cos x(1-sinx) +cos x(1+sinx)}/1-sinx^2
cos x-cosx sinx + cosx+ cosx sinx=2cosx
1-sinx^2=cosx^2
(2cosx)/(cosx^2) =2/cos x
term on right: tanx^2+ 1=secx^2. {sinx^2/cosx^2} +1 ={sinx^2+cosx^2/cosx^2} = 1/cosx^2=secx^2.
secx^2/sec x=sec x = 1/cos x
2* (1/cosx)= 2/cosx