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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)`
` rArr sec^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 = 0 rArr (t - 1/t)^2 +3/4 =0 therefore (dy)/(dx) = -1 AA x,y`
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