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If (sinx)(cosy)=1/2,t h e n(d^2y)/(dx^2)...

If `(sinx)(cosy)=1/2,t h e n(d^2y)/(dx^2)a t(pi/4,pi/4)` is `-4` (b) `-2` (c) `-6` (d) `0`

A

`-4`

B

`-2`

C

`-6`

D

0

Text Solution

Verified by Experts

`(sin x ) (cos y )=(1)/(2)`
`therefore" "(cos x ) (cos y) - sin y sin x (dy)/(dx) =0`
`"or "(dy)/(dx)=(cot x )(cot y)`
`"or "(d^(2)y)/(dx^(2))=-cosec^(2)xcdotcot y -cosec^(2)y cot xcdot (dy)/(dx)`
`"Now, "((dy)/(dx))_(((pi//4,pi//4)))=1`
`"or "((d^(2)y)/(dx^(2)))_(((pi//4,pi//4)))=-(2) (1) -(2) (1) (1) =-4`
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