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If cot A.cot B=2, then what is the value...

If `cot A.cot B=2,` then what is the value of `cos(A+B)*sec(A-B)?`

A

`(1)/(2)`

B

`(2)/(3)`

C

1

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
A
Consider cos (A+B).sec (A-B)
`=(cos(A+B))/(cos(A-B))=(cosAcosB-sinAsinB)/(cosAcosB+sinAsinB)`
Divide Nr and Dr by sin A sinB,
`(cotAcotB-1)/(cotAcotB+1)=(2-1)/(2+1)=(1)/(3)`
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