Results 1 to 2 of 2

Math Help - Help Simplifying Trig Identities

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    11

    Post Help Simplifying Trig Identities

    I need some help simplifying these identities...

    #1 5(sec^2x - sin^2xsec^2x)

    #2 sin(π/2 - x)(- secx)

    and verifying this one...

    #1 cscθ/cotθ + tanθ = cosθ
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,908
    Thanks
    766
    Hello, adam456006!

    I need some help simplifying these expressions.

    (1)\;\;5\left(\sec^2\!x - \sin^2\!x\sec^2\!x\right)

    We have: . 5\left(\sec^2\!x - \sin^2\!x\underbrace{\sec^2\!x}_{\frac{1}{\cos^2\!  x}} \right) \;=\;5\left(\sec^2\!x - \underbrace{\frac{\sin^2\!x}{\cos^2\!x}}_{\tan^2\!  x}\right)

    . . . . . . . = \;5\underbrace{\left(\sec^2\!x - \tan^2\!x\right)}_{\text{This is 1}} \;=\;5\cdot1 \;=\;5



    (2)\;\;\sin\left(\tfrac{\pi}{2}- x\right)(-\sec x)

    We have: . \underbrace{\sin\left(\tfrac{\pi}{2}-x\right)}_{\text{This is }\cos x}\underbrace{(-\sec x)}_{-\frac{1}{\cos x}} \;=\;\cos x\left(-\frac{1}{\cos x}\right) \;=\;-1




    Verify this identity: . (1)\;\;\frac{\csc\theta}{\cot\theta + \tan\theta} \:= \:\cos\theta

    We have: . \frac{\dfrac{1}{\sin\theta}} {\dfrac{\cos\theta}{\sin\theta} + \dfrac{\sin\theta}{\cos\theta}}


    Multiply by \frac{\sin\theta\cos\theta}{\sin\theta\cos\theta}

    . . \frac{\sin\theta\cos\theta\left(\dfrac{1}{\sin\the  ta}\right)} {\sin\theta\cos\theta\left(\dfrac{\cos\theta}{\sin  \theta} + \dfrac{\sin\theta}{\cos\theta}\right)} \;=\;\frac{\cos\theta}{\underbrace{\cos^2\!\theta + \sin^2\!\theta}_{\text{This is 1}}} \;=\;\frac{\cos\theta}{1} \;=\;\cos\theta

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simplifying an equation using trig identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 28th 2010, 05:40 PM
  2. Simplifying using trig identities
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 3rd 2010, 08:54 AM
  3. Trig Identities - Simplifying
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 13th 2010, 09:20 AM
  4. simplifying identities
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: January 4th 2010, 06:23 PM
  5. Simplifying trig identities
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: October 15th 2009, 02:49 PM

Search Tags


/mathhelpforum @mathhelpforum