SOLUTION: prove that{{{ (secX-cosecX)/(secX+cosecX)}}} ={{{(tanX-1)/(tanX+1)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: prove that{{{ (secX-cosecX)/(secX+cosecX)}}} ={{{(tanX-1)/(tanX+1)}}}      Log On


   

Question 1043832: prove that+%28secX-cosecX%29%2F%28secX%2BcosecX%29 =%28tanX-1%29%2F%28tanX%2B1%29
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
sec x-csc x=(1/cos x)- (1/sin x)=(sin x-cos x)/cos x * sin x--numerator
sec x + csc x=(sin x + cos x)/cos x* sin x--denominator.
(sin x - cos x)/cos x * sin x divided by (sin x + cos x)/cos x* sin x
Now cancel just the sin x in both denominators.
(sin x- cos x)/cos x divided by (sin x+ cos x)/cos x
This is tan x-1/tan x +1