Results 1 to 9 of 9

Math Help - Prove that

  1. #1
    Junior Member
    Joined
    Jul 2009
    Posts
    68

    Prove that

    show that the value of
    [{sin^3(pi + theta)}/{cos ^3(pi/2 + theta)}] * [{cos^3(-theta)}/{sin^3(pi- theta)}] * [{tan(2pi-theta)}/{cosec^2theta}] *

    [{sec^2 (pi-theta)}/{sin(2pi + theta)}]
    is independent of theta

    my incomplete soln-
    [{sin^3(pi + theta)}/{cos ^3(pi/2 + theta)}]= -sin^3theta / sin^3theta
    [{cos^3(-theta)}/{sin^3(pi- theta)}] = cos^3 theta / sin^3 theta
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,829
    Thanks
    1602
    Just so that we're clear, are you asking to simplify

    \displaystyle \frac{\sin^3{\left(\pi + \theta\right)}}{\cos^3{\left(\frac{\pi}{2} + \theta\right)}}\cdot \frac{\cos^3{\left(-\theta\right)}}{\sin^3{\left(\pi - \theta\right)}}\cdot \frac{\tan{\left(2\pi - \theta\right)}}{\csc^2{\left(\theta\right)}} \cdot \frac{\sec^2{\left(\pi - \theta\right)}}{\sin{\left(2\pi + \theta\right)}}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2009
    Posts
    68
    Quote Originally Posted by Prove It View Post
    Just so that we're clear, are you asking to simplify

    \displaystyle \frac{\sin^3{\left(\pi + \theta\right)}}{\cos^3{\left(\frac{\pi}{2} + \theta\right)}}\cdot \frac{\cos^3{\left(-\theta\right)}}{\sin^3{\left(\pi - \theta\right)}}\cdot \frac{\tan{\left(2\pi - \theta\right)}}{\csc^2{\left(\theta\right)}} \cdot \frac{\sec^2{\left(\pi - \theta\right)}}{\sin{\left(2\pi + \theta\right)}}
    yeah exactly please help
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,829
    Thanks
    1602
    I would start by converting everything to sines and cosines, then applying some unit-circle trigonometric identities to simplify...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jul 2009
    Posts
    68
    Quote Originally Posted by Prove It View Post
    I would start by converting everything to sines and cosines, then applying some unit-circle trigonometric identities to simplify...
    as already mentioned i have simplified the first and the second part , 3rd and 4th are posing problem. i can understand that all the thetas will be cancelled out, but how?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,829
    Thanks
    1602
    For starters, convert EVERYTHING to sines and cosines, including the terms with tangents, secants and cosecants.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Jul 2009
    Posts
    68
    Quote Originally Posted by Prove It View Post
    For starters, convert EVERYTHING to sines and cosines, including the terms with tangents, secants and cosecants.
    alrite, i have done, but still one sin theta is not cancelling out, i checked it repeatedly.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,829
    Thanks
    1602
    Which one?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Jul 2009
    Posts
    68
    Quote Originally Posted by Prove It View Post
    Which one?
    my answer is coming -cossec theta, what to do now, i have to cancel thetas right?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove a/b and a/c then a/ (3b-7c)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 23rd 2010, 06:20 PM
  2. Prove this
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: September 15th 2009, 02:36 AM
  3. Replies: 2
    Last Post: August 28th 2009, 03:59 AM
  4. Please prove
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 7th 2009, 02:58 PM
  5. sum prove
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: February 18th 2009, 02:01 AM

Search Tags


/mathhelpforum @mathhelpforum