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If tanalpha,tan beta are roots of the eq...

If `tanalpha,tan beta` are roots of the equation `(1 + cos theta) tan^(2) x - lambda tan x = 1 - cos theta` where `theta in (0, (pi)/(2))` and `cos^(2) (alpha + beta) = (1)/(51)` then `lambda` is :

A

`5sqrt2`

B

`10sqrt2`

C

10

D

5

Text Solution

Verified by Experts

The correct Answer is:
B
`cos^(2) (alpha + beta) =(1)/(51) rArr tan^(2) (alpha + beta) = 50`
`rArr ((tan alpha + tan beta)/(1-tanalpha tan beta))^(2) = 50 , [((lambda)/(1+costheta))/((1-(costheta-1)/(costheta +1)))]^(2) = 50`
`[(lambda)/(2)]^(2) =50 , " " lambda^(2) = 200, " " lambda = 10 sqrt(2)`
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