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If tan(x+y)=e^(x+y), then (dy)/(dx)...

If `tan(x+y)=e^(x+y)`, then `(dy)/(dx)`

A

is always equal to -1

B

may or may not be equal to -1

C

`(dy)/(dx)` cannot be obtained

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`tan(x+y)=e^(x+y)`
`rArrsec^(2)(x+y)[1+(dy)/(dx)]=e^(x+y)[1+(dy)/(dx)]`
`therefore(dy)/(dx)=-1` or `1+e^(2(x+y))=e^(x+y)` ( not possible )
`1+t^(2)-t=0rArr(t-1/t)^(2)+3/4=0therefore(dy)/(dx)=-1AAx,y`
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