SOLUTION: Determine the specific solutions (if any) to the equation on the interval [0, 2π) -1 + tanθ = -sec^2 θ (Simply your answer. Type an exact answer, using π

Algebra ->  Trigonometry-basics -> SOLUTION: Determine the specific solutions (if any) to the equation on the interval [0, 2π) -1 + tanθ = -sec^2 θ (Simply your answer. Type an exact answer, using π       Log On


   

Question 1103329: Determine the specific solutions (if any) to the equation on the interval [0, 2π)
-1 + tanθ = -sec^2 θ
(Simply your answer. Type an exact answer, using π as needed. Use a comma to separate answers as needed)
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Since the equation involves tan(x) and sec^2(x), almost certainly the quickest way to the solutions is to use the identity sec%28x%29%5E2+=+tan%28x%29%5E2%2B1. Then the equation is

-1%2Btan%28x%29+=+-%28tan%28x%29%5E2%2B1%29
tan%28x%29%5E2%2B1-1%2Btan%28x%29+=+0
tan%28x%29%5E2%2Btan%28x%29+=+0
tan%28x%29%28tan%28x%29%2B1%29+=+0
tan%28x%29+=+0 or tan%28x%29+=+-1

tan(x) is 0 at 0 and pi; tan(x) is -1 at 3pi/4 and 7pi/4.

Answers: 0, 3pi%2F4, pi, 7pi%2F4