Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.

Trig identity question.?



3 Answers

  • 1 decade ago
    Favorite Answer

    LHS = 1 + tan^2 x

    LHS = (cos^2 x + sin^2 x) / cos^2 x

    LHS = 1 / cos^2 x

    LHS = RHS


  • 1 decade ago

    Take the Pythagorean Identity and divide both sides by cos^2 x.

    Pythagorean Identity: (sin^2 x +cos^2 x = 1).

  • 1 decade ago

    I am assuming you want to prove this identity. First, express everything in terms of sine and cosine.

    LS = 1 + tan^2(x)

    LS = 1 + sin^2(x) / cos^2(x)

    RS = 1 / cos^2(x)

    Next I when I start seeing sin^2 and cos^2 in a proof, I start thinking of using the Pythagorean identity. sin^2(x) + cos^2(x) = 1, for all x.

    To perform the addition on the left side, I need a common denominator, which in this case is cos^2(x).

    LS = cos^2(x)/cos^2(x) + sin^2(x) / cos^2(x)

    LS = [cos^2(x) + sin^2(x) ] / cos^2(x)

    Apply the Pythagorean identity to the numerator.

    LS = 1 / cos^2(x)

    LS = RS

    Therefore, proven.

Still have questions? Get your answers by asking now.