If an equation of a tangent to the curve y=cos(x+y) ,x€[-1,1+π] is x+2y=k then k=?

Question

hartnn · Answer

x+2y = k is the equation of tangent at which point on the curve??

is k = pi/2?

samigupta8 · Answer

No, the ans is π/4..

samigupta8 · Answer

And even how u came up with an ans...
When we are not even given at which point to the curve we have drawn a tangent..how did u found it?

hartnn · Answer

y' = -sin (x+y) (1+y')

y' is the slope of tangent = -1/2 

-1/2 = - sin (x+y) (+1/2)

sin (x+y) = 1 --> x+y = pi/2
cos (x+y) = y = 0 

x= pi/2, y = 0 

x+2y = k = pi/2

hartnn · Answer

not sure how many rules did i break doing all these steps :P

samigupta8 · Answer

Ans is π/4 though.....

samigupta8 · Answer

It is true that ans given is π/4 
Bt i can't find a fault in your method...
:)

hartnn · Answer

with k = pi/4 you don't even get a real point of intersection, http://www.wolframalpha.com/input/?i=arccos+y+%2B+y+%3D+pi%2F4

phi · Answer

Not to beat a dead horse, but pi/4 appears to be a typo?

hartnn · Answer

yes, 
she confirmed that k = pi/2 is correct and not k=pi/4