Math Is Fun Forum

Breal607

Member

Registered: 2008-11-17

Posts: 3

Trigonemery Identities

The problem is.....

cos4 x sin3 x = (cos4 x - cos6 x)sinx
     ^       ^             ^          ^       

(^) means to rise the nuber as a power...

i just cant seem to find where to start this problem at????

Breal607

Member

Registered: 2008-11-17

Posts: 3

Re: Trigonemery Identities

Some other problems that im having trouble on are....

sec4 x - tan4 x = 1 + 2tan2x
     ^         ^                    ^

tan x sin2x = 2 - 2cos2 x
                               ^

csc x sin 2x - sec x = cos 2x sec x

2cos2 x/2 tan x = tan x + sin x
      ^             

tan 4x = (2tan 2x)/(2 - sec2 2x)
                                      ^

(^) Same as before...Denotes a power...

Any help would be appreciated...I have no idea what i am doing here...

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Trigonemery Identities

You can trade two cosines for two sines or vice versa, along with a constant.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Breal607

Member

Registered: 2008-11-17

Posts: 3

Re: Trigonemery Identities

Thanks for the help ricky. I solved the first one using your advice but if anyone has any answers about the other that would help greatly...

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Trigonemery Identities

There are two variants of Ricky's formula, obtained by dividing it by sin² and cos² respectively.
For example, dividing every term by sin²(x) gives:

Doing a similar thing but dividing by cos²(x) gets you another identity, and that one can be used to help with your second question.

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Why did the vector cross the road?
It wanted to be normal.

G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: Trigonemery Identities

The first identity is not valid cos4x*sin4x is not equal to  (cos4x-cos6x)*sinx

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Se Zoti vete e tha me goje,se kombet shuhen permbi dhe,por SHqiperia do te roje,per te,per te luftojme ne.
God said that all nation exincts on the ground,but Albania will survive,for it,for it we are fighting.

G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: Trigonemery Identities

You have to proof that

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Se Zoti vete e tha me goje,se kombet shuhen permbi dhe,por SHqiperia do te roje,per te,per te luftojme ne.
God said that all nation exincts on the ground,but Albania will survive,for it,for it we are fighting.

G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: Trigonemery Identities

2cos2 x/2 tan x = tan x + sin x  is not valid

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Se Zoti vete e tha me goje,se kombet shuhen permbi dhe,por SHqiperia do te roje,per te,per te luftojme ne.
God said that all nation exincts on the ground,but Albania will survive,for it,for it we are fighting.

G_Einstein

Member

Registered: 2008-08-30

Posts: 124

Re: Trigonemery Identities

Mathxpert says that the other identities are not valid.I'm note quite sure because I have no time to look by myself to proove the identities.I could proov just the previous identities.Try to use other identitities to proove the others .

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Se Zoti vete e tha me goje,se kombet shuhen permbi dhe,por SHqiperia do te roje,per te,per te luftojme ne.
God said that all nation exincts on the ground,but Albania will survive,for it,for it we are fighting.