SOLUTION: 1/cosA+sinA+1 + 1/cosA+sinA-1 is equal to cosecA+secA how to prove it.

Algebra ->  Trigonometry-basics -> SOLUTION: 1/cosA+sinA+1 + 1/cosA+sinA-1 is equal to cosecA+secA how to prove it.      Log On


   

Question 976140: 1/cosA+sinA+1 + 1/cosA+sinA-1 is equal to cosecA+secA how to prove it.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the more complicated expression and simplify.

1%2FcosA%2BsinA%2B1%2B1%2FcosA%2BsinA-1


You have obvious other simplifications to do first.
1%2Fcos%28A%29%2Bsin%28A%29%2Bsin%28A%29%2B1%2Fcos%28A%29%2B1-1, based on Commutative Property for Addition

2%2Fcos%28A%29%2B2sin%28A%29%2B0

2%2Fcos%28A%29%2B2sin%28A%29

Simplest common denominator is cos(A).

2%2Fcos%28A%29%2B%282sin%28A%29%2Acos%28A%29%29%2Fcos%28A%29

highlight_green%28%282%2B2sin%28A%29cos%28A%29%29%2Fcos%28A%29%29
This appears not to be same as cosec(A)+sec(A).

Try starting with the other expression instead.
csc%28A%29%2Bsec%28A%29
1%2Fsin%28A%29%2B1%2Fcos%28A%29
cos%28A%29%2F%28sin%28A%29cos%28A%29%29%2Bsin%28A%29%2F%28sin%28A%29cos%28A%29%29
highlight_green%28%28cos%28A%29%2Bsin%28A%29%29%2F%28sin%28A%29cos%28A%29%29%29

Much work done so far, but the identity is not proved, and it is likely not an identity.