SOLUTION: plz help verify this equation. just need the steps. (sin x - cos x/sin x) + (cos x - sin x/ cos x) = 2 - (sec x)(csc x)

Algebra ->  Trigonometry-basics -> SOLUTION: plz help verify this equation. just need the steps. (sin x - cos x/sin x) + (cos x - sin x/ cos x) = 2 - (sec x)(csc x)      Log On


   

Question 864375: plz help verify this equation. just need the steps.
(sin x - cos x/sin x) + (cos x - sin x/ cos x) = 2 - (sec x)(csc x)
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
(sin x - cos x/sin x) + (cos x - sin x/ cos x) = 2 - (sec x)(csc x)
(sin x - cos x/sin x) + (cos x - sin x/ cos x)
LCM
%28cosx%28sinx-cosx%29%2Bsinx%28cosx-sinx%29%29%2F%28sinx%2Acosx%29

%28cosx%2Asinx-cos%5E2%28x%29-sin%5E2%28x%29%2Bcosx%2Asinx%29%2Fsinx%2Acosx%29

%28cosx%2Asinx-%28cos%5E2%28x%29%2Bsin%5E2%28x%29%29%2Bcosx%2Asinx%29%2Fsinx%2Acosx%29
cos^2(x)+sin^2(x)=1
%28cosx%2Asinx-1%2Bcosx%2Asinx%29%2Fsinx%2Acosx%29

+%28-1%2B2cosx%2Asinx%29%2F%28sinx%2Acosx%29
%28-1%2F%28sinx%2Acosx%29%29+%2B%282sinxcosx%2Fcosxsinx%29
+-secx%2Acosecx+%2B2
= RHS