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# argh more P3! watch

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1. who else can't wait til P3 is over!
I'm having trouble differentiating and integrating things like sin^2 (1/2x), tan^2 (2x) etc. Does anyone have some kind of list to help me?!

thanks x
2. Sounds like you need to know your trig identities.

cos2x = 2cos²x - 1
cos2x = 1 - 2sin²x

tan²x + 1 = sec²x
3. (Original post by jazzyj)
who else can't wait til P3 is over!
I'm having trouble differentiating and integrating things like sin^2 (1/2x), tan^2 (2x) etc. Does anyone have some kind of list to help me?!

thanks x
For differentiation of those, use the chain rule:

d/dx [(tan 2x)^2] = 2(tan 2x).2(sec 2x)^2 = 4tan 2xsec^2 2x

d/dx [(sin 0.5x)^2] = 2(sin 0.5x).0.5cos 0.5x = sin 0.5xcos 0.5x

For integration, you use identities, as queen-of-pain said.
4. so because of the identity sin^2x + cos^2x = 1, does that work when it's sin^2 (2x) i.e. does sin^2 (2x) = 1 - cos^2 (2x)?
5. (Original post by jazzyj)
so because of the identity sin^2x + cos^2x = 1, does that work when it's sin^2 (2x) i.e. does sin^2 (2x) = 1 - cos^2 (2x)?
Yes.
6. (Original post by jazzyj)
who else can't wait til P3 is over!
I'm having trouble differentiating and integrating things like sin^2 (1/2x), tan^2 (2x) etc. Does anyone have some kind of list to help me?!

thanks x
Cos2x=1-ssin^2x therefore:

(1-cos2x)/2 =sin^2x

x=(x/2) therefore

(1-cosx)/2 = sin^2(x/2) then just integrate (1-cosx)/2 = (x-sinx)/2 + c

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