Yahoo Answers: Answers and Comments for Prove math 10 points? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20171021071655AAq9ub0
From Christopher
enUS
Sat, 21 Oct 2017 07:16:55 +0000
3
Yahoo Answers: Answers and Comments for Prove math 10 points? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20171021071655AAq9ub0
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From Snugglebunnie101: OK, here you go sweetheart :)
The first two ...
https://answers.yahoo.com/question/index?qid=20171021071655AAq9ub0
https://answers.yahoo.com/question/index?qid=20171021071655AAq9ub0
Sat, 21 Oct 2017 08:36:46 +0000
OK, here you go sweetheart :)
The first two questions are relatively straightforward!
1) Prove (cos2B+cos2A)/(cos2Bcos2A) = cot(A+B)cot(AB)
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(AB)
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=20120718014836AA1xoQV
Hope this helps !!!!!!!!!!!!!!!!!!!!!!!!