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# C 4 maths question watch

1. Can someone help me with question 6 i

2. (Original post by eggfriedrice)
Can someone help me with question 6 i

Use trig identities.
cos^x+sin^2x=.....?
3. (Original post by m4ths/maths247)
Use trig identities.
cos^x+sin^2x=.....?
I have, I keep ending up with tanx
4. Other hints:
Spoiler:
Show
for (i) as well as trig identities, notice the change from dx to dθ and for (ii) you will need the double angle formula so cos(2θ)=cos^2(θ)-sin^2(θ) You'll also need to fiddle with trig identities to get that identity in terms of just sin^2(θ) and cos(2θ)

Good luck!

Edit:
(Original post by eggfriedrice)
I have, I keep ending up with tanx
The d(x) changes to a d(θ) - so what you've done is right, just need to finish off.
5. (Original post by dragonrabbit)
Other hints:
Spoiler:
Show
for (i) as well as trig identities, notice the change from dx to dθ and for (ii) you will need the double angle formula so cos(2θ)=cos^2(θ)-sin^2(θ) You'll also need to fiddle with trig identities to get that identity in terms of just sin^2(θ) and cos(2θ)

Good luck!

Edit:

The d(x) changes to a d(θ) - so what you've done is right, just need to finish off.
I still don't get it. :| I didn't realise changing dx to dθ affected it? I'm pretty sure I haven't been taught this unless it's just something you're supposed to know?
6. (Original post by eggfriedrice)
I still don't get it. :| I didn't realise changing dx to dθ affected it? I'm pretty sure I haven't been taught this unless it's just something you're supposed to know?
Ask your teachers when you get back, you should have been/be taught this I think.

Basically, the dx determines what you are integrating/differentiating. So if it's dx - you are integrating with respect to x Because you've used the substitution x=sin^2(θ) - your integral is no longer in terms of x, but is now in terms of θ. Therefore integrating by dx doesn't affect what you have - in order to integrate it you need to change the dx to a dθ.
To do this: You go back to your original substitution x=sin^2(θ) If you differentiate that you get dx/dθ=2sin(θ)cos(θ). Then you can multiply the dθ over to the other side (I've been told that although dx/dθ isn't an actual fraction, you can treat it as one) to get dx=2sin(θ)cos(θ) dθ. You can then sub this back into your integral to end up with something just in terms of θ. Hope this helps. You'll need to simplify some more with double angle formula/identities.
7. (Original post by dragonrabbit)
Ask your teachers when you get back, you should have been/be taught this I think.

Basically, the dx determines what you are integrating/differentiating. So if it's dx - you are integrating with respect to x Because you've used the substitution x=sin^2(θ) - your integral is no longer in terms of x, but is now in terms of θ. Therefore integrating by dx doesn't affect what you have - in order to integrate it you need to change the dx to a dθ.
To do this: You go back to your original substitution x=sin^2(θ) If you differentiate that you get dx/dθ=2sin(θ)cos(θ). Then you can multiply the dθ over to the other side (I've been told that although dx/dθ isn't an actual fraction, you can treat it as one) to get dx=2sin(θ)cos(θ) dθ. You can then sub this back into your integral to end up with something just in terms of θ. Hope this helps. You'll need to simplify some more with double angle formula/identities.
I understand now! Thanks for the explanation.

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