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If alpha, beta are roots of the equation...

If `alpha, 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

`5sqrt(2)`

B

`10 sqrt(2)`

C

10

D

5

Text Solution

Verified by Experts

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