Prelim 2016 Maths Help Thread (2 Viewers)

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Green Yoda

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help:
prove that
(sin^2(a)*cos^2(b))-(cos^2(a)*sin^2(b))=sin^2(a)-sin^2(b)
 

InteGrand

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bruh this is purely 2u yr 11 trig.......I dunno differentiation yet lol
Can you do it another way?
Yes. (Sorry, forgot this was in prelim thread and you hadn't learnt calculus yet.)
 

clareh08

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If in 2014, the Australias population was 23 246 692, with a growth rate of approximately 1.14%, what was the population in 2015?

Please help! What is the formula and how would you work out this question
 

KingOfActing

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If in 2014, the Australias population was 23 246 692, with a growth rate of approximately 1.14%, what was the population in 2015?

Please help! What is the formula and how would you work out this question
Unless there's something I'm missing, isn't it just 23,246,692*(1+0.0114) = 23511704.3, and since you can't have 0.3 of a person, the answer is 23,511,704



Here the initial measurement was 23 246 692, and 1 year passed.
 

Green Yoda

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Help:
prove sin^2(θ)tan(θ)+cos^2(θ)cot(θ)+2sin(θ)cos(θ) = tan(θ)+cot(θ)

My working out so far:
LHS=(1-cos^2(θ))tan(θ)+cos^2(θ)cot(θ)+2sin(θ)cos(θ)
=tan(θ)-sin(θ)cos(θ)+cos^2(θ)cot(θ)+2sin(θ)cos(θ)
=tan(θ)+cos^2(θ)cot(θ)+sin(θ)cos(θ)
 

parad0xica

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Help:
prove sin^2(θ)tan(θ)+cos^2(θ)cot(θ)+2sin(θ)cos(θ) = tan(θ)+cot(θ)

My working out so far:
LHS=(1-cos^2(θ))tan(θ)+cos^2(θ)cot(θ)+2sin(θ)cos(θ)
=tan(θ)-sin(θ)cos(θ)+cos^2(θ)cot(θ)+2sin(θ)cos(θ)
=tan(θ)+cos^2(θ)cot(θ)+sin(θ)cos(θ)
cos^2 = 1 - sin^2 and you are done
 

KingOfActing

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Help:
prove sin^2(θ)tan(θ)+cos^2(θ)cot(θ)+2sin(θ)cos(θ) = tan(θ)+cot(θ)

My working out so far:
LHS=(1-cos^2(θ))tan(θ)+cos^2(θ)cot(θ)+2sin(θ)cos(θ)
=tan(θ)-sin(θ)cos(θ)+cos^2(θ)cot(θ)+2sin(θ)cos(θ)
=tan(θ)+cos^2(θ)cot(θ)+sin(θ)cos(θ)
You're almost there. Continuing on:

 

Green Yoda

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I have the worked our solution and they did some weird shit...
final answer: 3tan(θ)-tan^2(θ)/1-3tan^2(θ)
 
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