SOLUTION: Explain the following as an algebraic expression of a single trigonometric function: ((tan^2(a)-1)/(1+tan(a)) A)1+sec(a) B)tan(a)-1 C)1-sec(a) D)tan(a)+1

Algebra ->  Trigonometry-basics -> SOLUTION: Explain the following as an algebraic expression of a single trigonometric function: ((tan^2(a)-1)/(1+tan(a)) A)1+sec(a) B)tan(a)-1 C)1-sec(a) D)tan(a)+1      Log On


   

Question 888595: Explain the following as an algebraic expression of a single trigonometric function:
((tan^2(a)-1)/(1+tan(a))
A)1+sec(a)
B)tan(a)-1
C)1-sec(a)
D)tan(a)+1
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28sin%28a%29%2Fcos%28a%29%29%5E2-1%29%2F%281%2Bsin%28a%29%2Fcos%28a%29%29

%28%28sin%28a%29%2Fcos%28a%29%29%5E2-1%29%2F%281%2Bsin%28a%29%2Fcos%28a%29%29*%28cos%5E2%28a%29%2Fcos%5E2%28a%29%29

%28sin%5E2%28a%29-cos%5E2%28a%29%29%2F%28cos%5E2%28a%29%2Bsin%28a%29cos%28a%29%29, you can see difference of squares in the numerator, and factorability of the denominator.


Note the understood use of commutative property of addition...



%28sin%28a%29-cos%28a%29%29%2Fcos%28a%29

sin%28a%29%2Fcos%28a%29-cos%28a%29%2Fcos%28a%29

Tangent minus One.