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If ( sin x) (cos y) = 1//2, then d^(2)y/...

If ( sin x) (cos y) = `1//2,` then `d^(2)y//dx^(2)` at `(pi//4, pi//4)` is

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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