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Math Help - trig compound angle formulae and proofs

  1. #1
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    Red face trig compound angle formulae and proofs

    Hi I've got some maths homework and stuck on the last 3 questions.

    1. Given that sinA=3/5 and cosB=12/13, where A is obtuse and B is acute, find exact values of
    a) cos(A+B)
    b)cot (A-B)

    2. Prove cot(A+B)is identical to cotAcotB-1
    cotA+cotB
    3. prove that tanA+tanB is identical to sin(A+B)
    cosAcosB

    I have tried all these and just get stuck .

    any help would be really appreciative

    thankyou
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  2. #2
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    1) \cos A=-\sqrt{1-\sin^2A}, \ \sin B=\sqrt{1-\cos^2B}

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

    \cot(A-B)=\frac{\cos(A-B)}{\sin(A-B)}=\frac{\cos A\cos B+\sin A\sin B}{\sin A\cos B-\sin B\cos A}

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

    =\frac{\frac{\cos A\cos B}{\sin A\sin B}-1}{\frac{\sin A\cos B}{\sin B\sin A}+\frac{\sin B\cos A}{\sin A\sin B}}=\frac{\cot A\cot B-1}{\cot A+cot B}

    3) \tan A+\tan B=\frac{\sin A}{\cos A}+\frac{\sin B}{\cos B}=\frac{\sin A\cos B+\sin B\cos A}{\cos A\cos B}=\frac{\sin(A+B)}{\cos A\cos B}
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  3. #3
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    thankyou

    thanks so much. not sure if i get questions 1 yet though, i'll try it.
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