Results 1 to 4 of 4

Math Help - prove the following identities.

  1. #1
    Member
    Joined
    Oct 2009
    Posts
    202

    prove the following identities.

    please help me with this question:

    a) \frac{cot\theta}{tan\theta}+1=cosec^2\theta


    b) \frac{1+sin\theta}{cos\theta}+\frac{cos\theta}{1+s  in\theta}=2 sec\theta.

    please help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,518
    Thanks
    1404
    a) \frac{\cot{\theta}}{\tan{\theta}} + 1 = \frac{\cot{\theta}}{\frac{1}{\cot{\theta}}} + 1

     = \cot^2{\theta} + 1

     = \csc^2{\theta}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,518
    Thanks
    1404
    b) \frac{1 + \sin{\theta}}{\cos{\theta}} + \frac{\cos{\theta}}{1 + \sin{\theta}} = \frac{\cos{\theta}(1 + \sin{\theta})}{\cos^2{\theta}} + \frac{\cos{\theta}(1 - \sin{\theta})}{(1 + \sin{\theta})(1 - \sin{\theta})}

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

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

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

     = \frac{\cos{\theta} + \cos{\theta}\sin{\theta} + \cos{\theta} - \cos{\theta}\sin{\theta}}{\cos^2{\theta}}

     = \frac{2\cos{\theta}}{\cos^2{\theta}}

     = \frac{2}{\cos{\theta}}

     = 2\sec{\theta}.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    b) Maybe a shorter route...

    \frac{1+sin\theta}{cos\theta} + \frac{cos\theta}{1+sin\theta} = \frac{(1 + sin\theta)^2 + cos^2\theta}{cos\theta(1+sin\theta)}

     = \frac{1 + 2sin\theta + sin^2 \theta + cos^2\theta}{cos\theta(1+sin\theta)}}

     = \frac{2(1+sin\theta)}{cos\theta(1+sin\theta)}

     = \frac{2}{cos\theta}

     = 2sec\theta
    Last edited by Unknown008; June 22nd 2010 at 11:39 PM. Reason: Forgot a bracket in the first line after 1 + sin\theta
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Can't prove these identities?
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: November 20th 2010, 07:07 AM
  2. Prove Identities
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 26th 2010, 10:42 PM
  3. Prove these identities.
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: July 20th 2009, 09:42 PM
  4. prove identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: June 25th 2009, 11:08 PM
  5. Prove the following identities.............
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: July 16th 2008, 08:07 AM

Search Tags


/mathhelpforum @mathhelpforum