SOLUTION: Find the solution, if possible. {{{(1 + tan^2(theta))/(1+cos^2(theta))=tan^2(theta)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Find the solution, if possible. {{{(1 + tan^2(theta))/(1+cos^2(theta))=tan^2(theta)}}}      Log On


   

Question 1085324: Find the solution, if possible.
%281+%2B+tan%5E2%28theta%29%29%2F%281%2Bcos%5E2%28theta%29%29=tan%5E2%28theta%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%281+%2B+tan%5E2%28theta%29%29%2F%281%2Bcos%5E2%28theta%29%29=tan%5E2%28theta%29

1+%2B+tan%5E2%28theta%29=%281%2Bcos%5E2%28theta%29%5E%22%22%29tan%5E2%28theta%29





Multiply both sides by cos2q

1=%281%2Bcos%5E2%28theta%29%5E%22%22%29expr%28sin%5E2%28theta%29%29

1=%281%2Bcos%5E2%28theta%29%5E%22%22%29%281-cos%5E2%28theta%29%29

1=1-cos%5E4%28theta%29

cos%5E4%28theta%29=0

cos%5E%22%22%28theta%29=0

theta+=+%282n-1%29expr%28pi%2F2%29

But that is extraneous because the original equation
contains tan2(q) which is not defined for theta+=+%282n-1%29expr%28pi%2F2%29.

There is no solution.

Edwin