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Let cos(alpha + beta) = 4//5 and let si...

Let `cos(alpha + beta) = 4//5 ` and let `sin ( alpha - beta)= 5//13`, where `0 le alpha, beta lt pi//4`. Then `tan 2 alpha ` is equal to

A

`19//12`

B

`20//7`

C

`25//16`

D

`56//33`

Text Solution

Verified by Experts

The correct Answer is:
D
We have,
`cos(alpha+beta)=4/5and sin(alpha-beta)=5/13`n
`impliestan(alpha+beta)=3/5and tan(alpha-beta)=15/12`
`thereforetan 2alpha=tan(alpha+beta+alpha-beta)=(tan(alpha+beta)+an(alpha-beta))/(1-tan(alpha+beta)tan(alpha-beta))`
`impliestan 2alpha=((3)/(5)+(5)/(12))/(1-(3)/(5)xx(5)/(12))=56/33`
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