Results 1 to 3 of 3

Math Help - Help Prove trig identities

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    7

    Help Prove trig identities

    i have 3 questions that i need help on for my test tommorw, so if you could answer any of them that would be great, thanks

    prove each identity so L.S. = R.S.

    1) sin x/2 = 1-cosx/2 (right side of equation is all under square root sign)



    2)sin[cubed]x + cos[cubed]x = (1-sinxcosx)(sinx+cosx)

    3) sin(squared)M [csc(squared)M + sec(squared)M] = sec(squared)M

    any help is 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, getem j!

    2)\;\;\sin^3\!x + \cos^3\!x \:=\: (1-\sin x\cos x)(\sin x+\cos x)

    \underbrace{\sin^3\!x + \cos^3\!x}_{\text{sum of cubes}} \;=\;(\sin x + \cos x)(\sin^2\!x - \sin x\cos x + \cos^2\!x)

    . . . . . . . . . = \;(\sin x + \cos x)(\underbrace{\sin^2\!x + \cos^2\!x}_{\text{This is 1}} - \sin x\cos x)

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



    3)\;\;\sin^2\!x(\csc^2\!x + \sec^2\!x) \:=\: \sec^2\!x

    \text{Multiply: }\;\sin^2\!x(\csc^2\!x + \sec^2\!x) \;\;=\;\;\underbrace{\sin^2\!x\csc^2\!x}_{\text{Th  is is 1}} + \sin^2\!x\sec^2\!x \;\;=\;\;1 \;+\; \sin^2\!x\cdot\frac{1}{\cos^2\!x}

    . . . . . . = \;\;1 + \frac{\sin^2\!x}{\cos^2\!x} \;\;=\;\;1 + \left(\frac{\sin x}{\cos x}\right)^2 \;\;=\;\;1 + \tan^2\!x \;\;=\;\;\sec^2\!x

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    7
    thanks again Soroban

    you have ne suggestions for the first one?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove some identities!
    Posted in the Math Challenge Problems Forum
    Replies: 105
    Last Post: December 29th 2010, 11:58 PM
  2. Using y''+y=0 to prove trig identities
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: March 16th 2010, 11:59 AM
  3. Prove trig identities Help !!
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 21st 2009, 06:29 AM
  4. Trig Identities - Simplify and Prove
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 7th 2008, 03:14 PM
  5. trig - prove identities
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 4th 2008, 01:11 PM

Search Tags


/mathhelpforum @mathhelpforum