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Let cos (alpha+beta) = 4/5 and sin(alph...

Let ` cos (alpha+beta) = 4/5` and `sin(alpha-beta)=5/13 ` where `0<= alpha,beta<= pi/4` then find ` tan (2alpha)`

A

`(20)/(7)`

B

` ( 25)/(16) `

C

`(56)/(33)`

D

`(19)/(12)`

Text Solution

Verified by Experts

The correct Answer is:
C
`cos (alpha + beta )=(4)/(5)`
`rArr tan (alpha + beta) = (3)/(4)`
`" " sin (alpha - beta) = (5)/(13)`
`rArr tan (alpha - beta) = (5)/(12)`
` therefore tan 2 alpha = tan (alpha + beta + alpha - beta)`
` " "= ((3)/(4)= (5)/(12))/(1-(3)/(4)(5)/(12)) = (56)/(33)`
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