Matematika

Pertanyaan

1. 2tanx per 1+ tan2x=
2. 1+tan2x per 1-tan2x =
1. 2tanx per 1+ tan2x= 2. 1+tan2x per 1-tan2x =

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1 Jawaban

  • 1) 2 tanx / 1+tan^2x
    = 2 . (sinx /cosx) / sec^2x
    = 2 . (sinx /cosx) / 1/cos^2x
    = 2 .( sinx/cosx . cos^2x)
    = 2 sinx cosx

    2) 1+tan^2x / 1- tan^2x
    = 1+ (sin^2x / cos^2x) / 1- (sin^2x / cos^2x)
    =(cos^2x+sin^2x/cos^2x) / (cos^2x-sin^2x/ cos^2x)
    = ( cos^2x + sin^2x / cos^2x) . ( cos^2x / cos^2x - sin^2x)
    = cos^2x + sin^2x / cos^2x -sin^2x
    = 1 / cos^2x -sin^2x

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