Results 1 to 2 of 2

Math Help - Proving identities.

  1. #1
    Junior Member
    Joined
    Apr 2010
    Posts
    53

    Proving identities.

    {1-cos(2t)}/{cos(t)sin(t)} = 2tan(t)

    and

    {1/(1-sin(t))} + {1/(1+sin(t))} = 2sec^2(t)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member sbhatnagar's Avatar
    Joined
    Sep 2011
    From
    New Delhi, India
    Posts
    200
    Thanks
    17

    Re: help with trig problems please!!!

    Do you know that \cos{2x}=\cos^2{x}-\sin^2{x}?

    Prove \frac{1-\cos{2t}}{\cos(t)\sin(t)}=2\tan{t}
    In \frac{1-\cos{2t}}{\cos(t)\sin(t)}, substitute \cos{2t}=\cos^2{t}-\sin^2{t} and 1=\cos^2{t}+\sin^2{t}

    \\ \frac{1-\cos{2t}}{\cos(t)\sin(t)}=\frac{\cos^2{t}+\sin^2{t  }-\cos^2{t}+\sin^2{t}}{\cos(t)\sin(t)}=\frac{2\sin^2  {t}}{\sin{t}\cos{t}}=2\frac{\sin{t}}{\cos{t}} \\\\=  2\tan{t}

    Prove \frac{1}{1-\sin{t}}+\frac{1}{1+\sin{t}}=2\sec^2{t}
    Note that : \frac{1}{1-\sin{t}}+\frac{1}{1+\sin{t}}=\frac{1+\sin{t}+1-\sin{t}}{(1-\sin{t})(1+\sin{t})}=\frac{2}{1-\sin^2{t}}

    Substitute: 1-\sin^2{t}=\cos^2{t} and you will get the answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving identities 2
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: December 22nd 2011, 04:10 PM
  2. Proving Identities
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: June 6th 2011, 10:52 AM
  3. Replies: 6
    Last Post: June 23rd 2010, 12:59 AM
  4. proving identities....
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 2nd 2009, 11:21 PM
  5. Please help me with my proving identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 4th 2008, 03:22 AM

Search Tags


/mathhelpforum @mathhelpforum