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Trignometry

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 Joined: 28 Jul 2012 Post: 2
30 Jul 2012 21:34:33 IST
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b-c/b+c cotA/2 + b+c/b-c tanA/2 = 2cosec(B-C)
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

b-c/b+c cotA/2 + b+c/b-c tanA/2 = 2cosec(B-C)

Blazing goIITian

Joined: 22 May 2009
Posts: 2467
2 Aug 2012 11:41:18 IST
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basics:a/sinA=b/sinB=c/sinC=2R----------------------- 1

sinA+sinB=2sin{(A+B)/2}cos{(A-B)/2}---------2

sinA-sinB=2cos{(A+B)/2}sin{(A-B)/2}----------3

refer to above 1

we get {(sinB-sinC)/(sinB+sinC)}*cotA/2+{(sinB+sinC)/(sinB-sinC)}*tanA/2

using 2 & 3

we get tan(B-C)/2+cot(B-C)/2

by converting to sin & cos and solving we get 2csc(B-C)

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