# Trig Identities could sum1 pleas help

1. Sep 14, 2006

### ku1005

Hi, in this question i am nt sure the best way to tackle it!!
it follows

proove the following

2sinxcosx=sqrt(3)-ssqrt(3)sin^2x for 0<=x<=360

i tried using the doble angle formulae on the right, putting all on one side therfore =0 (anticipating a quadratic equation)
having

sin2x-sqrt(3)+2sqrt(3)sin^2(x)

i can see that a quadratic equation is smhow possible, but dont know how to get it there....any help or tips would be greatly apprecitaed!!!

thanks!

2. Sep 14, 2006

### ku1005

actually the double angle formulae on the left.....

3. Sep 14, 2006

### Pyrrhus

is the identity?

$$2 \sin x \cos x = \sqrt{3} - \sqrt{3} \sin^{2} x$$

because the above equation is not an identity.

4. Sep 14, 2006

### ku1005

sorry...not an identity...was readin the wrong stuff...it just wants me to solve for x

5. Sep 14, 2006

### Integral

Staff Emeritus
I don't think you need to go that route.

factor $\sqrt {3}$ from the RHS. Do you see anything that looks familiar?

6. Sep 14, 2006

### ku1005

u mean how the (1-2sin^2x) becomes (1-2(1-cos^2x)???
hang on i will see how that works

7. Sep 14, 2006

### ku1005

which then looks like double angle formulae for cos

8. Sep 14, 2006

### ku1005

gerat thanks very muc...get it down to tan2x=sqrt(3) thanks for ur help

9. Sep 14, 2006

### Integral

Staff Emeritus
Did you get all of the solutions?

My last question was in reference to the ORIGINAL equation. You do not need to use a double angle relationship to solve this.

10. Sep 14, 2006

### ku1005

ohh kk...dunno um i got all the soltutions.... so thanks, also this is a real common identity whih i am trying to proove

sin2x=2tanx/(tan^2x+1)

i am trying yo simplify the RHS,but evertyhing i do makes it more complicated...i must be missing somthing simple...hat should i start with??

11. Sep 15, 2006

### Pyrrhus

one huge hint:

$$\tan ^{2} x + 1 = \sec ^{2} x$$

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