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    Hi, Could someone please explain to me how/why these two expressions are eqivilent. Im having trouble understanding how the power of 3/2 is interacting with the cos^2(x).

    Any help is greatly appreciated! Thanks!

    \[\int \frac{cos(x)}{cos^2(x)^\frac{3}{  2}}d(x)) \equiv \int sec^2(x)d(x)\]
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    (Original post by Jonsmith98)
    Hi, Could someone please explain to me how/why these two expressions are eqivilent. Im having trouble understanding how the power of 3/2 is interacting with the cos^2(x).

    Any help is greatly appreciated! Thanks!

    \[\int \frac{cos(x)}{cos^2(x)^\frac{3}{  2}}d(x)) \equiv \int sec^2(x)d(x)\]
     cos^2(x) is just (cos(x))^2, use index laws.
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    (Original post by Jonsmith98)
    Hi, Could someone please explain to me how/why these two expressions are eqivilent. Im having trouble understanding how the power of 3/2 is interacting with the cos^2(x).

    Any help is greatly appreciated! Thanks!

    \[\int \frac{cos(x)}{cos^2(x)^\frac{3}{  2}}d(x)) \equiv \int sec^2(x)d(x)\]
    Adding onto what the 2nd reply said, this will make the fraction cos(x)/cos^6/2(x) which will simplify to cos(x)/cos^3(x) which will become 1/cos^2(x) which is the same as sec^2(x)
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    (Original post by bakedbeans247)
    Adding onto what the 2nd reply said, this will make the fraction cos(x)/cos^6/2(x) which will simplify to cos(x)/cos^3(x) which will become 1/cos^2(x) which is the same as sec^2(x)
    Ahhh I see now, thank you so much! Very helpful!
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    (Original post by Jonsmith98)
    Ahhh I see now, thank you so much! Very helpful!
    No worries, but i think you may find this helpful. Basically, you know examsolutions.net? I'm sure you do Well it has a Facebook group which is a very good place to ask any maths questions! Seriously you can get some really quick responses on their sometimes! so here's the link to it:

    https://www.facebook.com/groups/math...examsolutions/
 
 
 
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