Results 1 to 3 of 3

Math Help - Simplify expression and Identity

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    11

    Exclamation Simplify expression and Identity

    I still cant get the right answer for:

    (15tanXcscX-3cscX)/(9tanXcscX-3cscX)
    the choices are
    A)5/3 B)5/3 sinX+cosX C) (5sinX-cosX)/(3sinX-cosX) D) 5/3 sinX-cosX


    Also this problem

    1-(cos^2X/1+sinX)=sinX

    And finally
    (1-sin^2X)/(sinX-cscX)= -sinX
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,548
    Thanks
    541
    Hello, Amanda!

    \frac{15\tan x\csc x-3\csc x}{9\tan x\csc x-3\csc x}

    . . (A)\;\tfrac{5}{3}\qquad(B)\;\tfrac{5}{3}\sin x + \cos x \qquad(C)\;\frac{5\sin x-\cos x}{3\sin x-\cos x}\qquad(D)\;\tfrac{5}{3}\sin x-\cos x

    Factor and reduce: . \frac{3\csc x(5\tan x - 1)}{3\csc x(3\tan x - 1)} \;=\;\frac{5\tan x - 1}{3\tan x - 1} \;=\;\frac{5\,\dfrac{\sin x}{\cos x} - 1}{3\,\dfrac{\sin x}{\cos x} -1}

    Multiply by \frac{\cos x}{\cos x}\!:\;\;\frac{\cos x\left(5\,\frac{\sin x}{\cos x} - 1\right)}  {\cos x\left(3\,\frac{\sin x}{\cos x} - 1\right)} \;=\;\frac{5\sin x - \cos x}{3\sin x - \cos x} . . . answer (C)



    1 - \frac{\cos^2\!x}{1+\sin x} \:=\:\sin x

    The left side is: . 1 - \frac{1-\sin^2\!x}{1+\sin x} \;\;=\;\;1 - \frac{(1-\sin x)(1+\sin x)}{1 + \sin x}

    . . = \;\;1 - (1 - \sin x) \;\;=\;\;1 - 1 + \sin x \;\;=\;\;\sin x



    \frac{1-\sin^2\!x}{\sin x-\csc x}\:=\: -\sin x

    The left side is: . \frac{1-\sin^2\!x}{\sin x - \csc x} \;=\; \frac{\cos^2\!x}{\sin x - \frac{1}{\sin x}}

    Multiply by \frac{\sin x}{\sin x}\!:\;\;\frac{\sin x}{\sin x}\cdot\frac{\cos^2\!x}{\sin x - \frac{1}{\sin x}} \;=\;\frac{\sin x\cos^2\!x}{\sin^2\!x - 1} \;=\;\frac{\sin x\cos^2\!x}{-(1-\sin^2\!x)}

    . . . . = \;\frac{\sin x\cos^2\!x}{-\cos^2\!x} \;=\;\frac{\sin x}{-1} \;=\;-\sin x

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2009
    Posts
    11
    THANK YOU SOOOOOOOOOOOO MUCH!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How do I simplify this expression?
    Posted in the Algebra Forum
    Replies: 1
    Last Post: April 1st 2010, 01:46 AM
  2. simplify this log expression
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: March 28th 2010, 07:06 PM
  3. Simplify the expression #2
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 21st 2009, 01:51 PM
  4. simplify expression
    Posted in the Algebra Forum
    Replies: 2
    Last Post: May 16th 2008, 03:28 AM
  5. Simplify Expression
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: May 9th 2008, 02:35 PM

Search Tags


/mathhelpforum @mathhelpforum