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Math Help - Verify the following identity

  1. #1
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    Verify the following identity

    tanČA+cscČA = cotČA+secČA

    AND

    secA-1 = sinČ(A)/cosA+cosČA

    How would these be done?
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  2. #2
    MHF Contributor red_dog's Avatar
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    1) \tan^2A+\csc^2A=\frac{\sin^2A}{\cos^2A}+\frac{1}{\  sin^2A}=\frac{\sin^4A+\cos^2A}{\sin^2A\cos^2A}=

    =\frac{(1-\sin^2A)^2+\cos^2A}{\sin^2A\cos^2A}=\frac{1-\cos^2A+\cos^4A}{\sin^2A\cos^2A}=

    =\frac{\sin^2A+\cos^4A}{\sin^2A\cos^2A}=\frac{1}{\  cos^2A}+\frac{\cos^2A}{\sin^2A}=\sec^2A+\cot^2A

    2) \frac{\sin^2A}{\cos A+\cos^A}=\frac{1-\cos^2A}{\cos A(1+\cos A)}=\frac{(1-\cos A)(1+\cos A)}{\cos A(1+\cos A)}=

    =\frac{1-\cos A}{\cos A}=\sec A-1
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