SOLUTION: The equation below can be made into an identity and simplified completely as shown. cos(u) sec (u)/tan (u) = f(u)/g(u) a) f(u) = b) g(u) =

Algebra ->  Trigonometry-basics -> SOLUTION: The equation below can be made into an identity and simplified completely as shown. cos(u) sec (u)/tan (u) = f(u)/g(u) a) f(u) = b) g(u) =       Log On


   

Question 826810: The equation below can be made into an identity and simplified completely as shown.
cos(u) sec (u)/tan (u) = f(u)/g(u)
a) f(u) =
b) g(u) =
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
cos%28u%29+sec%28u%29%2Ftan%28u%29+=+f%28u%29%2Fg%28u%29
Since cos and sec are reciprocals of each other and since the product of reciprocals is always a 1, this simplifies to:
1%2Ftan%28u%29+=+f%28u%29%2Fg%28u%29
The left side is the reciprocal of tan(u). Since cot(u) is also the reciprocal of tan(u) we can substitute it in:
cot%28u%29+=+f%28u%29%2Fg%28u%29
Since cot%28u%29=cos%28u%29%2Fsin%28u%29 we can substitute for it:
cos%28u%29%2Fsin%28u%29+=+f%28u%29%2Fg%28u%29
So f(u) = cos(u) and g(u) = sin(u).