More trigonometric identities

The first one is fine, since cot = cos/sin = (1/sin)/(1/cos) = cosec/sec. The second one is wrong. cos^2 + sin^2 = 1, but that doesn't mean that 1/cos^2 + 1/sin^2 = 1. In fact, 1/cos^2 t + 1/sin^2 t = (cos^2 t + sin^2 t)/(cos^2 t sin^2 t) = 4cosec^2 (2t).
 
FrostedNipple said:
Am i right in thinking

cotθ = cosecθ / secθ

and

cosec^2θ + sec^2θ = 1
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First one:
Since 1/tanθ = cosθ/sinθ
1/tanθ = (1/sinθ) / (1/cosθ)
1/tanθ = (1/sinθ) * cosθ
1/tanθ = cosθ/sinθ
So the first one is correct.

Forgot how to prove the second one. Let me do it on paper first, i'll be back.
 
Also, it is easy to see that the second one is incorrect. For t just slightly larger than 0 sint is very small, so cosec t is going to be very large, so for small t cosec t > 0). Clearly sec^2 >= 0, so cosec^2 t + sec^2 t > 1 for small t, so it certainly can't be true for all t.
 
Damn, I have found the World Alien Invasion Force (WAIF's) here on Earth.......we used to kill the kids who studied this at school.....what the hell happened to Neanderthalism......it seemed so perfect a regime!! :) :)
 
Dingo said:
Damn, I have found the World Alien Invasion Force (WAIF's) here on Earth.......we used to kill the kids who studied this at school.....what the hell happened to Neanderthalism......it seemed so perfect a regime!! :) :)
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They couldn't do their tax document due to lack of mathematical skill so were all fined massive amounts by the government, forced to live on the streets and all died out. Your next fool :)
 
Psiko said:
The first one is fine, since cot = cos/sin = (1/sin)/(1/cos) = cosec/sec. The second one is wrong. cos^2 + sin^2 = 1, but that doesn't mean that 1/cos^2 + 1/sin^2 = 1. In fact, 1/cos^2 t + 1/sin^2 t = (cos^2 t + sin^2 t)/(cos^2 t sin^2 t) = 4cosec^2 (2t).
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Dear lord!
 
FrostedNipple said:
I just thought it would work because

1/sin^2θ = cosec^2θ etc etc

1/sin^2θ + 1/cos^2θ = 1/1 obviously you can't do that though.
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No you can't. 1/x + 1/y does not equal 1/(x+y). For example 1/2 + 1/2 does not equal 1/(2+2) = 1/4. Instead you have to "cross-multiply". ie. 1/x + 1/y = y/xy + x/xy = (x+y)/xy. Then 1/2 + 1/2 = (2+2)/(2*2) = 4/4 = 1 which is correct. Cross-multiplying just means getting both of the fractions over a common denominator, just like you would do when adding numeric fractions like 1/2 + 1/3.

Hope that helps.
 
FrostedNipple said:
They couldn't do their tax document due to lack of mathematical skill so were all fined massive amounts by the government, forced to live on the streets and all died out. Your next fool :)
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But I has a BIG club (with Conservative) written all down the side, to beat those NuLabour Tax Devils to death, skills we need don't need no brain or lernin, but honesty and true, We's gonna make an "old fashioned fortune", wiv dem boys in Blue!! :)

Tax is Red in colour
Black the hue of strife
Green, for envy of the educate
But Blue if yoose want a life

You foolin no-one
Wiv your nips as cold as Ice
Dem Labour Monkeys
Never heard of de word Thrice

Have your tax documents
De education of de Brown
Tis you my friend, who will
Be acting as his clown
 
Voltar said:
what are these ancient symbols useful for exactly? (NOT trolling btw)
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Compared to a lot of stuff in modern day maths, they actually could be. anyway i prefer statistics, Statistics was such a good GCSE to do, i took 1 hour after school once a week for a year and got an A and all the matsh you knew you could apply later in real life. Such a good subject.
 
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