Results 1 to 2 of 2

Math Help - Trig Identities Help

  1. #1
    Newbie
    Joined
    May 2009
    Posts
    4

    Trig Identities Help

    1. tan(x+(pi/2)) = -cotx
    2. cos^2(x) = csc^2(x)-cot^2(x) / sec^2(x)
    3. cosx + cosxtan^2(x) = secx

    I'm just not good with this stuff. I tried expanding the left side of the first one using sum and difference formulas and got no where with it, and for the other two I just got everything in terms of sin and cos and got even more lost. Any help is greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Hello, College Student!

    1)\;\;\tan\left(x+\tfrac{\pi}{2}\right) \:=\: -\cot x
    \tan\left(x+\tfrac{\pi}{2}\right) \;=\;\frac{\sin(x + \frac{\pi}{2})}{\cos(x + \frac{\pi}{2})}\;=\;\frac{\sin x\cos\frac{\pi}{2} + \cos x\sin\frac{\pi}{2}} {\cos x\cos\frac{\pi}{2} - \sin x\sin\frac{\pi}{2}}\;= . \frac{\sin x\cdot 0 + \cos x\cdot1}{\cos x\cdot0 - \sin x\cdot1} \;=\;\frac{\cos x}{\text{-}\sin x} \;=\;-\cot x


    2)\;\;\cos^2\!x \:= \:\frac{\csc^2\!x-\cot^2\!x}{\sec^2\!x}
    \text{On the right: }\;\frac{\overbrace{\csc^2\!x - \cot^2\!x}^{\text{This is 1}}}{\sec^2\!x} \;=\;\frac{1}{\sec^2\!x} \;=\;\cos^2\!x


    3)\;\;\cos x + \cos x\tan^2\!x \:=\: \sec x
    \text{Factor: }\cos x\overbrace{(1 + \tan^2\!x)}^{\text{This is }\sec^2\!x} \;=\;\cos x\!\cdot\!\sec^2\!x \;=\;\overbrace{(\cos x\!\cdot\!\sec x)}^{\text{This is 1}}\sec x \;=\;\sec x

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trig Identities
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 3rd 2009, 07:44 AM
  2. Trig identities
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: June 22nd 2009, 07:58 AM
  3. Trig Identities
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 9th 2008, 05:35 PM
  4. Trig Identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 7th 2008, 09:25 PM
  5. Trig Identities Help!!!!
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: April 14th 2008, 12:47 PM

Search Tags


/mathhelpforum @mathhelpforum