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

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

A

`cosAcosB=(1)/(5)`

B

`sinAsinB=-(2)/(5)`

C

`cosAcosB=-(1)/(5)`

D

`sinAsinB=-(1)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
A
`therefore5 cos(A-B)=(3)/(5)`
`therefore5cosAcosB+5sinAsinB=3` (i)
From `2^(nd)` relation,
`sin AsinB=2cosAcosB` (ii)
`thereforecosAcosB=(1)/(5)and5((1)/(2)+1)sinAsinB=3`
`sinAsinB=(2)/(5)`
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