# Maths

Prove that: (sinx-2sin2x+sin3x)/(sinx+2sin2x+sin3x)= -tan^2 x/2.

1. 👍 0
2. 👎 0
3. 👁 154
1. sinx + sin3x = 4sinx cos^2x = 2sin2x cosx

So, you have

(2sin2x cosx - 2sin2x)
---------------------------
(2sin2x cosx + 2sin2x)

2sin2x(cosx-1)
---------------------
2sin2x(cosx+1)

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

Now take a look at the half-angle formula for tan(x/2)

1. 👍 0
2. 👎 0
posted by Steve
2. I don't understand it....

1. 👍 0
2. 👎 0
posted by Mahlatse
3. tan^2(x/2) = (1-cosx)/(1+cosx)

1. 👍 0
2. 👎 0
posted by Steve

## Similar Questions

1. ### maths

proof that (sinx+sin3x-2sin2x)/(sinx+sin3x+2sin2x)=-tan(x/2)

asked by thato on April 6, 2016
2. ### Trigonometric

sin3x=(sinx)(3-asin^2x) Wow! is that arcsin^2(x) ??? are we solving for x? or is it proving the identity? proving the identity sin3x=(sinx)(3-sin^2x) Your identity is wrong, it should say: sin3x=(sinx)(3-4sin^2x) try this: sin(3x)

asked by abdo on May 3, 2007
3. ### maths

prove that cos3x+sin3x/cos x-sin x=1+2sin2x

asked by sunny on July 22, 2009
4. ### Trig

Prove the following functions: (sinx+sin2x)/(1+cosx+cos2x)=tan x (cos3x/sinx)+(sin3x/cosx)=2cot2x tan2x=(2/cotx-tanx) theses are due in the am. Fastness would be great?

asked by jared on November 7, 2011
5. ### Maths

Prove By induction that sinx + sin3x + sin5x +.... Sin(2n-1) =sin^2(nx)/sin3x

asked by Joel on September 7, 2016
6. ### Trig Help

Prove the following: [1+sinx]/[1+cscx]=tanx/secx =[1+sinx]/[1+1/sinx] =[1+sinx]/[(sinx+1)/sinx] =[1+sinx]*[sinx/(sinx+1)] =[sinx+sin^2x]/[sinx+1] =[sinx+(1-cos^2x)]/[sinx+1] =??? This is where I'm stuck. Can someone help me.

asked by Anonymous on March 11, 2012
7. ### trigonometry

Prove: sin3x-sinx/cos3x-cosx=-cot2

asked by Dini on November 2, 2010
8. ### trigonometry

prove: sinx/sec2x+cosx/csc2x=sin3x

asked by liger on October 31, 2014
9. ### Trig........

I need to prove that the following is true. Thanks (cosx / 1-sinx ) = ( 1+sinx / cosx ) I recall this question causing all kinds of problems when I was still teaching. it requires a little "trick" L.S. =cosx/(1-sinx) multiply top

asked by abdo on April 18, 2007
10. ### trig

how does this work? (Sin2x+cos2x+2sinĀ²x)/(sinx+cosx) = (sinx+cosx

asked by Tim on May 29, 2008

More Similar Questions