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Prelim 2016 Maths Help Thread (3 Viewers)

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integral95

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yeah I know but which is the best to take?
The rule of thumb is when you have 1-cos(2x) you end up with 2sin^2(x)
And 1+cos(2x) gives 2cos^2(x)

You'll nee those identities when you learn to integrate sin^2(x) as well in the future.

Otherwise when you have cos(2x) by itself there is no rule of thumb. There's more intuition required for those. e.g. difference of two squares may mean I leave it in the original form cos^2(x)-sin^2(x)
essentially the identity to remove the value 1.
 

eyeseeyou

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1.cot(x+y)=(cot x cot y -1)/(cot x + cot y)
2.(tan 2theta-tan theta)/(tan2 theta +cot theta)=tan squared theta
3. (1-tan theta than 2 theta)/(1=tantheta than 2 theta)= 4 cos^2 theta -3
 

Drongoski

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Are you serious...

What do you think?
I started on cos(4x) is that LHS or RHS

cos(4x) = 1 - 2 cos^2(2x) by double angle

And then another double angle to come
Incorrect.

2cos2 2x = 1 + cos 4x
 

integral95

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1.cot(x+y)=(cot x cot y -1)/(cot x + cot y)
2.(tan 2theta-tan theta)/(tan2 theta +cot theta)=tan squared theta
3. (1-tan theta than 2 theta)/(1=tantheta than 2 theta)= 4 cos^2 theta -3
???

for Q 2

you use the double angle formula for both (tan 2theta), then you go through the tedious algebra to simplify to the RHS. (hint multiply top and bottom by (1-tan^2)(tan))
 

Trebla

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Ugh. Ok never doing maths again whilst on alcohol.
Doing a 'simple' but thought heavy maths question is a great test to see how sobered up you are after drinking
 
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