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If cos(alpha+beta)=(4)/(5)andsin(alpha-b...

If `cos(alpha+beta)=(4)/(5)andsin(alpha-beta)=(5)/(13)`, were `0le,betale(pi)/(4)`, then tan `2alpha` is equal to

A

`(25)/(16)`

B

`(56)/(33)`

C

`(19)/(12)`

D

`(20)/(7)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given ,`cos(alpha+beta)=(4)/(5)`
`rArralpha+betain` Ist quadrant and `sin(alpha-beta)=(5)/(13)`
`rArralpha-betain` Ist quadrant
`because2alpha=(alpha+beta)+(alpha-beta)`
`thereforetan2alpha=(tan(alpha+beta)+tan(alpha-beta))/(1-tan(alpha+beta)tan(alpha-beta))=((3)/(4)+(5)/(12))/(1-(3)/(4)*(5)/(12))=(56)/(33)`
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