# Maths Problem!!!

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#1
Im stuck into a large amount of revision for my P2 mock tommorow and have been fine until I came across this little question that I can't seem to answer properly...

1a) Given that: cos(X+30) = 3cos(X-30), prove that, tanX= -(sqrt3)/2

1b) Prove that, (1-cos2X) / (sin2X) = tanX

Any help on these would be much appreciated (and rewarded with rep)!!!
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16 years ago
#2
(Original post by Leekey)
1a) Given that: cos(X+30) = 3cos(X-30), prove that, tanX= -(sqrt3)/2
cos x cos 30 - sin x sin 30 = 3 cos x cos 30 + 3 sin x sin 30
4 sin x sin 30 = -2 cos x cos 30
sin x / cos x = -1/2 cos 30 / sin 30

tan x = -1/2 ((rt 3)/2)/(1/2 = - (rt 3) / 2
0
16 years ago
#3
1-cos(2x) = 2 sin^2 x.

So (1-cos2x) / sin 2x = 2sin^2 x / 2sinx cos x = sinx/cosx = tan x
0
16 years ago
#4
(Original post by Leekey)
1b) Prove that, (1-cos2X) / (sin2X) = tanX
1 - cos2x = sin²x + cos²x - (cos²x - sin²x) = 2 sin²x

sin 2x = 2 sin x cos x

=> (1-cos2x)/sin2x = (2 sinx sinx)/(2 sinx cosx) = sinx / cosx = tanx
0
16 years ago
#5
(Original post by Leekey)
Im stuck into a large amount of revision for my P2 mock tommorow and have been fine until I came across this little question that I can't seem to answer properly...

1a) Given that: cos(X+30) = 3cos(X-30), prove that, tanX= -(sqrt3)/2

1b) Prove that, (1-cos2X) / (sin2X) = tanX

Any help on these would be much appreciated (and rewarded with rep)!!!
this is your lucky day. i have da intermediate maths mock paper 2 with me now.
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#6
OK so elpaw will be recieving the rep for tonight BUT theone will be getting some some also because he was the first to reply with the answer to the second question!!!

Thankyou both very much, I can't believe that I couldn't do the first one. I can never prove the trig identities but I should have been able to use the sum and product formulae in the first one...ohhh well, back to revision...
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#7
(Original post by mikie)
this is your lucky day. i have da intermediate maths mock paper 2 with me now.
Wasn't aware that A2 maths had an intermediate paper...lol....I think you mean GCSE paper!!! If any of this stuff is on that paper then I am very impressed at the current level of our GCSE students!!!
0
16 years ago
#8
(Original post by Leekey)
OK so elpaw will be recieving the rep for tonight BUT theone will be getting some some also because he was the first to reply with the answer to the second question!!!

Thankyou both very much, I can't believe that I couldn't do the first one. I can never prove the trig identities but I should have been able to use the sum and product formulae in the first one...ohhh well, back to revision...

wooo i never cant get bak to revision once i get here or on internet, i always do this, i know i will regert later but i still do it or say cant help myself on it
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16 years ago
#9
Have you noticed? The maths dudes always take up teh questions no matter what. Especially quick when rep is around.
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16 years ago
#10
(Original post by 2776)
Have you noticed? The maths dudes always take up teh questions no matter what. Especially quick when rep is around.
hmmm, yes, i have noticed
0
16 years ago
#11
well i've solved my fair share of maths probs here (about 2 ), but have got jack all rep for it.......... not that it's that big a deal tho
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