SOLUTION: which of the following is equivalent to {{{(1-Cos^2theta)/(Cos^2theta)}}}? a){{{Sec^2theta}}} b){{{Csc^2theta-1}}} c){{{Tan^2theta}}} d){{{Sin^2theta}}} e){{{-1/(Sin^2theta)}}

Algebra ->  Trigonometry-basics -> SOLUTION: which of the following is equivalent to {{{(1-Cos^2theta)/(Cos^2theta)}}}? a){{{Sec^2theta}}} b){{{Csc^2theta-1}}} c){{{Tan^2theta}}} d){{{Sin^2theta}}} e){{{-1/(Sin^2theta)}}      Log On


   

Question 329702: which of the following is equivalent to %281-Cos%5E2theta%29%2F%28Cos%5E2theta%29?
a)Sec%5E2theta
b)Csc%5E2theta-1
c)Tan%5E2theta
d)Sin%5E2theta
e)-1%2F%28Sin%5E2theta%29
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
%281-Cos%5E2theta%29%2F%28Cos%5E2theta%29

There is an identity that goes Sin%5E2theta%2BCos%5E2theta=1 which can
be written as Sin%5E2theta=1-Cos%5E2theta
So replace the numerator by Sin%5E2theta
%28Sin%5E2theta%29%2F%28Cos%5E2theta%29
which can be written
%28Sin%28theta%29%2FCos%28theta%29%29%5E2
There is an identity that goes %28Sin%28theta%29%29%2F%28Cos%28theta%29%29=Tan%28theta%29
So the final answer is
%28Tan%28theta%29%29%5E2
or
Tan%5E2theta, choice c)
Edwin