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If cos(alpha+beta)=3/5, sin(alpha-beta)=...

If `cos(alpha+beta)=3/5, sin(alpha-beta)=5/13`, and `0 lt alpha, beta lt pi/4`, then `tan(2alpha)` is equal to:

A

`21/16`

B

`63/52`

C

`33/52`

D

`63/16`

Text Solution

Verified by Experts

The correct Answer is:
D
`tan(alpha+beta)=4/3" " tan (alpha-beta)=5/12`
`implies(alpha=beta)=ten^-1(4/3)" ".....(i)`
`implies(alpha=beta)=ten^-1(5/12)" ".....(ii)`
Adding (i)and (ii) we get,
`implies2alpha=ten^-1(4/3)+tan^-1(5/12)," " tan2alpha=(4/3+5/12)/(1-20/36)=63/16`
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