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Integration C4 Question

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    Just came across a question where it says to integrate:

    1/sec^2y

    I thought you'd do 1/(1+tan^2x) but that seems to complicate matters ?

    Would appreciate the help,

    Many thanks!
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    1/sec2y = cos2y

    this might help or I might be completely wrong xD
    I'm 80% sure this will will help though

    oh its a sqaured!
    yh intergrate cos^2y
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    (Original post by Jasmine_777)
    Just came across a question where it says to integrate:

    1/sec^2y

    I thought you'd do 1/(1+tan^2x) but that seems to complicate matters ?

    Would appreciate the help,

    Many thanks!
     \displaystyle \int \frac1{sec^2y} \ dy

    We know  \displaystyle sec^2y = \frac1{cos^2y}

    So the integral becomes,  \displaystyle \int \frac1{sec^2y} \ dy = \int cos^2y \ dy

    Now use the identity,  \displaystyle cos2y=2cos^2y-1
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    (Original post by raheem94)
     \displaystyle \int \frac1{sec^2y} \ dy

    We know  \displaystyle sec^2y = \frac1{cos^2y}

    So the integral becomes,  \displaystyle \int \frac1{sec^2y} \ dy = \int cos^2y \ dy

    Now use the identity,  \displaystyle cos2y=2cos^2y-1
    ooh doh! didn't see that.

    Thanks again!

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