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Trignometry

Blazing goIITian

Joined:	1 Jul 2007
Post:	301

19 Aug 2007 21:38:44 IST

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re:trigo doubt

None

sorry ,i mistyped the question earlier.the actual question is:

If cos(A-B)=3/5 and tan A.tan B=2,then

(a)cos A.cos B=1/5

(b)sin A.sin B=-2/5

(c)cos(A+B)=-1/5

(d)sin A.cos B=4/5

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Comments (3)

santhosh in NUS

Hot goIITian

Joined: 13 Aug 2007

Posts: 132

19 Aug 2007 21:58:27 IST

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OPTIONS

3 ARE CORRECT!!!

CHEERS!!!!!!!!

Ankur Verma

Blazing goIITian

Joined: 29 Mar 2007

Posts: 555

19 Aug 2007 22:15:00 IST

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cos(A - B) = 3/5

cosAcosB + sinAsinB = 3/5

divide by cosAcosB

cosAcosB = 3/5*1/(1 + tanAtanB)

cosAcosB = 1/5

sinAsinB = 3/5 - 1/5 = 2/5

cos(A + B) = 1/5 - 2/5 = -1/5

1 n 3 r correct hope u got it do rate me if helpfull

Bipin Dubey

Forum Expert

Joined: 23 Jan 2007

Posts: 7942

19 Aug 2007 22:55:18 IST

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tanA.tanB = 2

(sinA.sinB) / (cosA.cosB) = 2

sinA.sinB = 2cosA.cosB

Now cos(A-B)=3/5

cosA.cosB + sinA.sinB = 3/5

cosA.cosB + 2cosA.cosB = 3/5

cosA.cosB = 1/5............(1)

so sinA.sinB = 2cosA.cosB = 2/5.............(2)

cos(A+B) = cosA.cosB - sinA.sinB = 1/5 - 2/5 = -1/5...........(3)

so third option is correct.

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