Results 1 to 3 of 3

Math Help - Proving analytic trig

  1. #1
    Junior Member
    Joined
    Oct 2007
    Posts
    55

    Proving analytic trig

    1.
    (1/(1+sinx)) + (1/(1-sinx)) = 2SEC(X)^2

    2.1/(secx-tanx)= secx+tanx
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,

    For the first one, put the fractions of the left side on the same denominator. Then simplify with the cosē+sinē=1 formula


    For the second one, multiply the first term with 1-sin(x) on the numerator and denominator
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,857
    Thanks
    739
    Hello, bilbobaggins!

    1)\;\;\frac{1}{1+\sin x}  +  \frac{1}{1-\sin x} \;=\;2\sec^2\!x
    \frac{1}{1 + \sin x}\cdot{\color{blue}\frac{1-\sin x}{1-\sin x}} + \frac{1}{1-\sin x}\cdot{\color{blue}\frac{1+\sin x}{1+\sin x}} \;=\;\frac{1-\sin x}{1-\sin^2\!x} + \frac{1+\sin x}{1-\sin^2\!x}


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




    2)\;\;\frac{1}{\sec x-\tan x} \;=\;\sec x + \tan x
    \frac{1}{\sec x - \tan x}\cdot{\color{blue}\frac{\sec x + \tan x}{\sec x + \tan x}} \;=\;\frac{\sec x + \tan x}{\underbrace{\sec^2\!x-\tan^2\!x}_{\text{This is 1}}} \;=\;\sec x + \tan x

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving that an analytic function on a region is constant.
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 18th 2011, 06:42 PM
  2. Analytic Trig- Sin, Cos, Tan
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: January 19th 2009, 03:54 PM
  3. Analytic Trig
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 16th 2008, 11:40 PM
  4. Analytic Trig.
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 14th 2008, 11:14 AM
  5. analytic trig
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: February 26th 2008, 06:19 PM

Search Tags


/mathhelpforum @mathhelpforum