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Math Help - Trigonometric identity proof

  1. #1
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    Trigonometric identity proof

    Hi all, I am stuck on this problem. Help would be appreciated.

    Here's the identity I need to prove (will only take a sec to read):

    View image: Untitled

    Here's my attempt:


    http://s13.postimage.org/jkhubi4lz/DSC03534.jpg
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  2. #2
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    Re: Trigonometric identity proof

    Change the secant and cosecant to cosine and sine. Then use Sum-Product identity then simplify the expression.
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  3. #3
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    Re: Trigonometric identity proof

    Hello, Frederick!

    We are expected to know these two identities:

    . . \cos(A + B) \:=\:\cos A\cos B - \sin A\sin B

    . . \cos2A \:=\:\cos^2A - \sin^2A



    \text{Prove: }\:\frac{\cos3x}{\sec x} - \frac{\sin x}{\csc3x} \:=\:\cos^22x - \sin^22x

    We have: . \frac{\cos3x}{\sec x} - \frac{\sin x}{\csc3x} \;\;=\;\;\frac{\cos3x}{\frac{1}{\cos x}} - \frac{\sin x}{\frac{1}{\sin3x}} \;\;=\;\; \cos3x\cos x - \sin3x\sin x

    . . . . . . . . . =\;\;\cos(3x+x) \;\;=\;\;\cos 4x \;\;=\;\;\cos^22x - \sin^22x
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