Prove math 10 points?

1. (cos2B+cos2A)/(cos2B-cos2A)=cot(A+B)cot(A-B)

2. (cos2B-cos2A)/(sin2B+sin2A)=tan(A-B)

3. (sinA+2sin3A+sin5A)/(sin3A+2sin5A+sin7A)=sin3A/sin5A

Update:

Sorry there is technical prbm

here is:

1. = cot (A+B)cot(A-B)

3. =sin3A/sin5A

tq so much for helping!!!

1 Answer

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  • 2 years ago
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    OK, here you go sweetheart :)

    The first two questions are relatively straightforward!

    1) Prove (cos2B+cos2A)/(cos2B-cos2A) = cot(A+B)cot(A-B)

    Use the sum - product trig identities to obtain:

    cos2B + cos2A = 2cos(A + B)cos(A - B)

    cos2B - cos2A = 2sin(B + A)sin(A - B)

    LHS = [2cos(A + B)cos(A - B)] /[2sin(B + A)sin(A - B)]

    = cot(A + B)cot(A - B)

    = RHS, as required!

    2) Prove (cos2B - cos2A)/(sin2B+sin2A) = tan(A-B)

    Again, using the same steps as above we have the left - hand side as :

    cos2B - cos2A = 2sin(B + A)sin(A - B)

    sin2B + sin2A = 2sin(B + A)sin(A - B)

    LHS = [2sin(B + A)sin(A - B)] /[2sin(B + A)sin(A - B)]

    = sin(A - B) /cos(A - B)

    = tan(A - B)

    = RHS, as required!

    3) Now for this question, please consult the following resource (I don't have enough space on here to write my own solution!)

    https://answers.yahoo.com/question/index?qid=20120...

    Hope this helps !!!!!!!!!!!!!!!!!!!!!!!!

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