Post by: madoscar65 on December 28, 2010, 11:34:44 pm
I've been trying to solve this, but I end up no where near the answer... So I was just wondering if you guys can help :) . The question is, prove that cosecx+cotx=cot(x/2)
Thanks
Post by: cohen on December 29, 2010, 12:10:59 am
1/six(x) + cos(x)/sin(x) = (1 + cos(x))/sin(x)
as 1/sin(x) and cos(x)/sin(x) have the same denominator, we can simplify this to
(1 + cos(x))/sin(x) = (1 + cos(x))/sin(x)
LHS = RHS
For cot(x/2), i did 1/tan(x/2)
For useful trig identidies:
http://uppit.com/18umapw8cozi/TRIGONOMETRY_IDENTITIEs.pdf
Post by: ninbam1k on January 15, 2011, 10:17:30 am
cosec(x) +cot(x)
= 1/sin(x) + cos(x)/sin(x) = 1+cos(x)/ sin(x)
cos(x) = 2(cos(x/2))^2 - 1
sin(x) = 2sin(x/2)cos(x/2)
= 1 + 2(cos(x/2))^2 - 1/ 2sin(x/2)cos(x/2)
= 2(cos(x/2))^2 / 2sin(x/2)cos(x/2)
cos(x/2)/sin(x/2)
=cot(x/2)
Post by: pi on January 15, 2011, 10:38:14 am
For useful trig identidies:
http://uppit.com/18umapw8cozi/TRIGONOMETRY_IDENTITIEs.pdf
Holy crap... I wrote that sheet!
(This was my original link...)
Post by: ivanivan0002 on January 16, 2011, 07:54:54 pm
It is possible to find the solutions between [-p,p] for sec x = 2.5 without using a calculator?
Post by: brightsky on January 16, 2011, 08:16:23 pm
Post by: brightsky on January 16, 2011, 09:51:00 pm
What about the exact value of sin1? (degrees)
Sounds rather bashy...
Theoretically, yes, using this: http://en.wikipedia.org/wiki/Trigonometric_identity#Double-.2C_triple-.2C_and_half-angle_formulae. But seeing as the exact value of sin(3) is already quite OMG, re: http://en.wikipedia.org/wiki/Exact_trigonometric_constants...
Post by: ivanivan0002 on January 16, 2011, 11:36:52 pm
Solve each of the following equations [0,2p]
cos^2 x - cosxsinx = 0
sin2x = sinx
Post by: Andiio on January 16, 2011, 11:44:17 pm
i.e.
cosx (cosx - sinx) = 0
Then utilising the null factor, you get:
cos x = 0, cos x = sin x.
I'm sure you can solve it from there :)
2. sin 2x = sin x
Use the identity of sin 2x! :)
Post by: ivanivan0002 on January 17, 2011, 01:06:49 am
Post by: vea on January 17, 2011, 01:23:06 pm
1=tanx
Then you can solve from there.
Post by: ivanivan0002 on January 18, 2011, 12:51:53 pm
I'm getting pretty annoying but,
sin8x = cos4x, find all the solutions between [0,2p]
Would this involve compound formulas and factorising?
Post by: kamil9876 on January 18, 2011, 01:28:40 pm
Ahh...thanks alot vea!
I'm getting pretty annoying but,
sin8x = cos4x, find all the solutions between [0,2p]
Would this involve compound formulas and factorising?
Yes double angle formula is enough. If it makes it any easier you may want to let
So you need to solve over a big domain.
Then we get:
Now solve over the required domain as given above.