# math (trig)

i have some problems doing trig
the first one is: Show that cos(x/2) sin(3x/2) = ½(sinx + sin2x)
i know that you are supposed to substitute all those trig function things in it but i kind of forgot how to
the only that i can see substituting in is the double angle one for sin2x
could anyone walk me through the process maybe?

What a very nasty trig identity.

I am sure this is not the most efficient way, but the neat thing about identities, if you do legitimate steps, usually you end up showing LS = RS.

I end up with a lot of x/2 angles, so whenever I have one of those I will replace it with A

LS= cos(x/2)sin(3x/2)
=cosA(sin(x+x/2))
=cosA(sinxcos(x/2) + cosxsin(x/2))
=cosA(2sinAcosAcosA + (cos^2 A - sin^2 A)sinA)
= 2(sin^2 A)(cos^3 A + sinA(cos^3 A) - (sin^3 A)(cosA)
=(sinA(cosA)[(3cos^2 A) - (sin^2 A)]

let that one sit for a while

R.S.
= 1/2(2sinAcosA + 2sinxcosx_
=sinAcosA + sinxcosx
=sinAcosA + (2sinAcosA)(cosx)
=sinAcosA(1 + 2cosx)
=sinAcosA(1 + cosx + cosx)
=sinAcosA(sin^2A + cos^2A + 2cos^2A -1 + 1 - 2sin^2A)
= sinAcosA(3cos^2A - sin^2A)
= L.S. !!!!!!!!!

please, somebody come up with a better way.

1. 👍 0
2. 👎 0
3. 👁 205

## Similar Questions

1. ### Simplifying with Trigonometry Identities

Hi, I am a senior in High School having a really difficult time with two problems. I have to prove using the trigonometric identities that they equal each other but I am having a really hard time trying to get them to equal each

asked by amanda on March 7, 2007
2. ### TRIG!

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x +

asked by hayden on February 23, 2009
3. ### Mathematics - Trigonometric Identities - Reiny

Mathematics - Trigonometric Identities - Reiny, Friday, November 9, 2007 at 10:30pm (sinx - 1 -cos^2x) (sinx + 1 - cos^2x) should have been (sinx - 1 + cos^2x) (sinx + 1 - cos^2x) and then the next line should be sin^2x + sinx -

asked by Anonymous on November 10, 2007
4. ### Math (trigonometric identities)

I was given 21 questions for homework and I can't get the last few no matter how hard and how many times I try. 17. Sinx-1/sinx+1 = -cos^2x/(sinx+1)^2 18. Sin^4x + 2sin^2xcos^2x + cos^4x = 1 19. 4/cos^2x - 5 = 4tan^2x - 1 20. Cosx

asked by Kim on December 4, 2012
5. ### Trig

Simplify sin x cos^2x-sinx Here's my book's explanation which I don't totally follow sin x cos^2x-sinx=sinx(cos^2x-1) =-sinx(1-cos^2x) =-sinx(sin^2x) (Where does sine come from and what happend to cosine?) =-sin^3x

asked by Tara on January 4, 2010
6. ### Math

I need help solving for all solutions for this problem: cos 2x+ sin x= 0 I substituted cos 2x for cos^2x-sin^2x So it became cos^2(x)-sin^2(x) +sinx=0 Then i did 1-sin^2(x)-sin^2(x)+sinx=0 = 1-2sin^2(x)+sinx=0 = sinx(-2sinx+1)=-1

asked by Martha on February 26, 2017
7. ### trig

We are doing trig identities in school. I need help with these five: 1.1+sinx/1-sinx=cscx+1/cscx-1 2.tanx+sinx/1+cosx=tanx 3.sec^2x/sin^2x=1/sin^2x+1/cos^2x 4.tan^2x/1+tan^2x=1-cos^2x 5.sinx-sin^3x/cos^3x=tanx

asked by Jay on December 4, 2011
8. ### Precalculus/Trig

I can't seem to prove these trig identities and would really appreciate help: 1. cosx + 1/sin^3x = cscx/1 - cosx I changed the 1: cosx/sin^3x + sin^3x/sin^3x = cscx/1-cosx Simplified: cosx + sin^3x/sin^3x = cscx/1-cosx I don't

asked by Heather on August 15, 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 26

simplify to a constant or trig func. 1. sec ²u-tan ²u/cos ²v+sin ²v change expression to only sines and cosines. then to a basic trig function. 2. sin(theta) - tan(theta)*cos(theta)+ cos(pi/2 - theta) 3. (sec y - tan y)(sec y

asked by hilde on March 14, 2010

More Similar Questions