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If alpha and beta are acute such that al...

If `alpha` and `beta` are acute such that `alpha+beta` and `alpha-beta` satisfy the equation `tan^(2)theta-4tan theta+1=0`, then `(alpha, beta`) =

A

`(30^(@), 60^(@))`

B

`(45^(@),45^(@))`

C

`(45^(@),30^(@))`

D

`(60^(@),45^(@))`

Text Solution

Verified by Experts

The correct Answer is:
C
`tan^(2)theta-4 tan theta + 1=0`
`rArr tan theta = (4 pm sqrt(12))/(2)=2pm sqrt(3)`
`rArr tan (alpha+beta)=2+sqrt(3)` and `tan (alpha-beta)=2-sqrt(3)`
`rArr alpha+beta=75^(@)` and `alpha-beta =15^(@)`
`rArr alpha = 45^(@)` and `beta = 30^(@)`
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