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Math Help - Trig Identities

  1. #1
    tsaephenix
    Guest

    Exclamation Trig Identities

    Okay, this is all C3 (advanced maths, the English A-Level), and I need some help.

    I need to prove that sin/cos + cos/sin = 2cosec2x

    ... any ideas?

    I got this so far:

    2cosec2x

    2/sin2x

    2/2sinxcosx (2's cancel out)

    then from there, I think I'm stuck...

    Help!

    Luv me x x x
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  2. #2
    Super Member

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    Hello, tsaephenix!

    Prove that: . \frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} \:= \:2\csc2x

    Generally, we start with the more complicated side
    . . and try to simplify it to match the other side.

    The left side is: . \tan x + \cot x \:=\:\tan x + \frac{1}{\tan x} \;=\;\frac{\tan^2\!x+1}{\tan x} \;=\;\frac{\sec^2\!x}{\tan x}

    Then we have: . \frac{\frac{1}{\cos^2x}}{\frac{\sin x}{\cos x}} \:=\:\frac{1}{\sin x\cos x}\;=\;\frac{2}{2\sin x\cos x} \;=\;\frac{2}{\sin2x} \;=\;2\csc2x

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