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If y = sqrt((cos x - sin x)(sec 2x + 1)(...

If `y = sqrt((cos x - sin x)(sec 2x + 1)(cos x + sin x))` ,
Then `(dy)/(dx)` at `x = (5 pi)/(6)` is :

A

`(1)/(sqrt(2))`

B

`-(1)/(sqrt(2))`

C

`(sqrt(3))/(2)`

D

`-(sqrt(3))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
`y = sqrt((1 + cos 2x)/(cos 2 x). Cos 2x),` `y = sqrt(2 cos^(2) x)`
`y = sqrt(2) |cos x|`, At `x = (5pi)/(6), cos x lt 0`,
`:. Y = - sqrt(2) cos x`, `(dy)/(dx) = sqrt(2) (5 pi)/(6) = (1)/(sqrt(2))`
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