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Let y=ln(1+cosx)^2 . Then the value of (...

Let `y=ln(1+cosx)^2` . Then the value of `(d^2y)/(dx^2)+2/(e^(y/2))` equal

(a)0

(b) `2/(1+cosx)`

(c)`4/(1+cosx)`

(d) `(-4)/((1+cos"x")^2)`

A

0

B

`(2)/(1+cos x)`

C

`(4)/(1+ cos x)`

D

`(-4)/(1+ cos x)^(2)`

Text Solution

Verified by Experts

`y=2" In "(1+ cos x)`
`(dy)/(dx)=(-2 sin x)/(1+cos x)`
`(d^(2)y)/(dx^(2))=-2[((1+cos x)cos x- sin x(-sin x))/((1+cos x)^(2))]`
`=-2[(cos x +1)/((1+cos x)^(2))]=(-2)/((1+ cos x))`
`"Now, "2e^(-y//2)=2cdote^(-("In "(1+cos x)^(2))/(2))=(2)/((1+cos x))`
`therefore" "(d^(2)y)/(dx^(2))+(2)/(e^(y//2))=0`
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