Math Is Fun Forum

ragingkiwi

Member

Registered: 2008-04-22

Posts: 1

trig ident.

prove:

1/sinx -sinx = cosx/tanx

1-sinx/cosx = cosx/(1 + sinx)

1/tanx + tanx = 1/(sinxcosx)

(1-2sin^2x)/(cosx+sinx) = cosx-sinx

explanations for each one would be greatly appreciated.. and a few hints to get confident with these    thanks for help!

mleiner

Member

Registered: 2008-04-02

Posts: 2

Re: trig ident.

1/sinx - (sinx)^2/sinx
= 1 - (sinx)^2 / sinx
= (cosx)^2 / sinx
that is equal to cosx/tanx
tanx = sinx/cosx
cosx/(sinx/cosx)
= (cosx)^2 / sinx

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: trig ident.

#3.)
1/tanx + tanx = 1/(sinxcosx)
c/s + s/c = 1/sc
cc/sc + ss/sc = 1/sc
cc + ss = 1  Yes, that is pythagoreans theorm.

---

igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: trig ident.

#4.)
(1-2sin^2x)/(cosx+sinx) = cosx-sinx
(1 - 2s^2)/(c+s) = c-s
mult both sides by c+s:
1 - 2s^2 = (c+s)(c-s)       (do you remember diff between 2 squares?)
multiply the right side out to see the difference between 2 squares.
1 - 2s^2 = c^2 - s^2 + sc - cs   ( the sc - cs are is 0, they are the same)
s is sine      c is cos       so sc and cs are just sin*cos  or cos*sin
1 - 2s^2 = c^2 - s^2
Add 2s^2 to both sides:
1 = c^2 + s^2  True!, pythagorean's theorm again.

---

igloo myrtilles fourmis

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: trig ident.

#2.) 1-sinx/cosx = cosx/(1 + sinx)
This one cannot be proven because it is false, just try 22 degrees
on your calculator.
(see mathsyperson below me)

Last edited by John E. Franklin (2008-04-23 02:44:17)

---

igloo myrtilles fourmis

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: trig ident.

The left side of #2 is (1-sinx)/cosx, as opposed to 1-tanx. With those brackets, the identity works.

(1-sinx)/cosx
[(1-sinx)(1+sinx)]/[cosx(1+sinx)]
(1-sin²x)/[cosx(1+sinx)]
cos²x/[cosx(1+sinx)]
cosx/(1+sinx)

---

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

ragingkiwi

Member

Registered: 2008-04-22

Posts: 1

Re: trig ident.

woot! cheers guys