SOLUTION: Verify the identity. {{{((cscx+secx)/(sinx+cosx))=cosx+tanx}}} Quick help would be greatly appreciated.

Algebra ->  Trigonometry-basics -> SOLUTION: Verify the identity. {{{((cscx+secx)/(sinx+cosx))=cosx+tanx}}} Quick help would be greatly appreciated.      Log On


   

Question 746612: Verify the identity.
%28%28cscx%2Bsecx%29%2F%28sinx%2Bcosx%29%29=cosx%2Btanx
Quick help would be greatly appreciated.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%28csc%28x%29%2Bsec%28x%29%29%2F%28sin%28x%29%2Bcos%28x%29%29%22%22=%22%22cos%28x%29%2Btan%28x%29

Sorry, but that is not an identity.

I will show that it does not hold in the case of the 3-4-5 right
triangle, where x is the smaller acute angle:



%28csc%28x%29%2Bsec%28x%29%29%2F%28sin%28x%29%2Bcos%28x%29%29%22%22=%22%22cos%28x%29%2Btan%28x%29

%285%2F3%2B5%2F4%29%2F%283%2F5%2B4%2F5%29%22%22=%22%224%2F5%2B3%2F4

%2820%2F12%2B15%2F12%29%2F%287%2F5%29%22%22=%22%2216%2F20%2B15%2F20

%2835%2F12%29%2F%287%2F5%29%22%22=%22%2231%2F20

%2835%2F12%29%2A%285%2F7%29%22%22=%22%2231%2F20

%28cross%2835%29%5E5%2F12%29%2A%285%2Fcross%287%29%29%22%22=%22%2231%2F20

25%2F12%22%22=%22%2231%2F20

That is false, so the equation is not an identity

Edwin