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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's Avatar

Hot goIITian

Joined: 13 Aug 2007
Posts: 132
19 Aug 2007 21:58:27 IST
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OPTIONS
 
1
 
3 ARE CORRECT!!!
 
 
 
CHEERS!!!!!!!!
Ankur Verma's Avatar

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's Avatar

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Joined: 23 Jan 2007
Posts: 7942
19 Aug 2007 22:55:18 IST
2 people liked this

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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