1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Sin^4Ө =3/8-3/8cos(2Ө) Prove the following trigonometric identity

  1. Aug 13, 2015 #1
    1. The problem statement, all variables and given/known data
    Prove the following trigonometric identity. The question is sin^4Ө =3/8-3/8cos(2Ө)

    2. Relevant equations
    I think I'm supposed to use the power reducing formulas for trigonometric identities which are
    sin^2(u)= (1- cos(2u))/2
    *Let u represent any integer/value*

    3. The attempt at a solution
    To expand the equation I separated the equation into (1- cos^2Ө)(1- cos^2Ө) = 1- 2cos^2Ө + (cos^2Ө)^2. I reduced it because sin^2Ө = 1 – cos^2Ө and after this I'm confused on what the next steps are.
  2. jcsd
  3. Aug 13, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    So, a much better post than the first try. Good !

    Your other entry is from the righthand side: what have you got for ##\cos(2\theta)## that might be useful here ?

    [edit] ah: your second relevant equation !
  4. Aug 13, 2015 #3


    Staff: Mentor

    So you applied the sin^2(u) to the lefthand side of the equation and got (1/4) * (1 - cos(2u) )^2 right?

    Next expand the

    (1/4)*(1 - cos(2u) )^2 = (1/4) * ( 1 - 2*cos(2u) - cos(2u)^2 )

    next apply the cos^2(u) rule to the last term and see what you get.
  5. Aug 13, 2015 #4
    As well as the power reducing formulas, you'll want to glance at the double angle formulas.
  6. Aug 13, 2015 #5


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    But now I see a problem coming up:
    let ##\theta = \pi/2\ \ ## then ##(sin\theta)^4 = 1\ \ ## and ##\ \ 3/8-3/8\cos(2\theta)=3/4## !?
    So no identity at all !
    Or did I read the original thingy in the wrong way ?
  7. Aug 13, 2015 #6


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I believe the identity ought to read ##\sin^4(\theta)=\frac 38-\frac 12\cos(2\theta)+\frac 18\cos(4\theta)##.
    Looks like someone turned that ##4\theta## into another ##2\theta##.
  8. Aug 14, 2015 #7


    User Avatar

    Why would u have to be an integer?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted