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Core 3 (AQA), need help with part of a question.

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!

Unparseable latex formula:

\[\int \frac{cos(x)}{cos^2(x)^\frac{3}{2}}d(x)) \equiv \int sec^2(x)d(x)\]

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!

Unparseable latex formula:

\[\int \frac{cos(x)}{cos^2(x)^\frac{3}{2}}d(x)) \equiv \int sec^2(x)d(x)\]



cos2(x) cos^2(x) is just (cos(x))2(cos(x))^2, use index laws.
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!

Unparseable latex formula:

\[\int \frac{cos(x)}{cos^2(x)^\frac{3}{2}}d(x)) \equiv \int sec^2(x)d(x)\]



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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Jonsmith98
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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!
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 :wink: 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/mathsrevision.examsolutions/

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