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Math Help - Trig Functions

  1. #1
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    Trig Functions

    I was wondering if someone could please take a look at my numbers 12 and 21...I need to simplify them so that the right and left sides are equal...but I am stuck on these final two problems...could anyone please assist me?

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  3. #3
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    Hello, aikenfan!

    12)\;\frac{\cot^3\!x}{\csc t} \:=\:\cos t(\csc^2\!t - 1)
    We have: . \frac{\cot t}{\csc t}\cdot\cot^2\!t \;\;=\;\;\frac{\dfrac{\cos t}{\sin t}}{\dfrac{1}{\sin t}} \cdot\cot^2\!t \;\;=\;\;\cos t\cot^2\!t \;\;=\;\;\cos t(\csc^2\!t - 1)


    21)\;\csc x - \cos x \:=\:\sin x\tan x
    This one has a typo . . . It is not true.

    It's probably: . {\color{blue}\sec x} - \cos x \:=\:\sin x\tan x

    On the left: . \frac{1}{\cos x} - \cos x \;\;=\;\;\frac{1-\cos^2\!x}{\cos x} \;\;=\;\;\frac{\sin^2\!x}{\cos x} \;\;=\; \;\sin x\cdot\frac{\sin x}{\cos x} \;\;=\;\;\sin x\tan x

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