SOLUTION: Simplify and write the trigonometric expression in terms of sine and cosine: ((2+tan^(2)x)/(sec^(2)x))−1=(f(x))^2

Algebra ->  Trigonometry-basics -> SOLUTION: Simplify and write the trigonometric expression in terms of sine and cosine: ((2+tan^(2)x)/(sec^(2)x))−1=(f(x))^2      Log On


   

Question 1104113: Simplify and write the trigonometric expression in terms of sine and cosine:
((2+tan^(2)x)/(sec^(2)x))−1=(f(x))^2
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


%282%2Btanx%5E2%29%2Fsecx%5E2-1

%282%2B%28sinx%5E2%29%2Fcosx%5E2%29%2F%281%2Fcosx%5E2%29-1 ... get everything in terms of sinx and cosx

%28%282cosx%5E2%2Bsinx%5E2%29%2Fcosx%5E2%29%2F%281%2Fcosx%5E2%29-1 ... combine terms in the numerator

2cosx%5E2%2Bsinx%5E2-1 ... multiply numerator and denominator by cosx^2

1%2Bcosx%5E2-1 ... using sinx^2+cosx^2=1

cosx%5E2

Since the problem appears to want us to write the simplified trig expression as f(x)^2, I suppose the answer they want is
f%28x%29+=+cosx