Does cos + sin always equal 0?

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The discussion clarifies that the equation cos + sin does not equal zero in a general sense. It emphasizes that sine and cosine are functions without inherent values, and the equation can only hold true under specific conditions, such as sin(2nπ) + cos(π/2 + nπ) = 0. The relationship cos(x) = -sin(x) is highlighted as a condition for equality, while the fundamental identity cos²(x) + sin²(x) = 1 is also referenced.

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does cos + sin = 0?
 
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cos + sin can never be equal to anything other than cos + sin. sin and cos are just functions. Neither has a "value" as such.

Do you want to if sin(somevalue1) + cos(somevalue2) = 0?
 
Ry122 said:
does cos + sin = 0?

like neutrino said cos + sin have no meaning. But if we get let's say

sin(2n pi)+ cos[(pi/2)+n pi] =0, and there are more samples like this. if this is what you meant at first place?
 
did you mean cosx+sinx=0 ?
\mbox{for the above to be true},\\ cosx=-sinx \\ \Rightarrow cotx=-1 (or sinx=0 but this does not hold for that.)
 
Please only post calculus questions in this forum.
 
ChaoticLlama said:
Please only post calculus questions in this forum.
LOL,this may well be calculus...
Max(sinx+cosx)= \sqrt{2}
Min(sinx+cosx)= -\sqrt{2}
Since they function is continuous, it must have x such that f(x)=0
 
To OP: Short answer. No.
 
Wait up, perhaps you got confused with this:

\cos^2 x + \sin^2 x = 1
 

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