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asinx+bcosx=c and a+b=2. if the given equation has a solution for all real values of a, then number of integral values of c are?

asinx+bcosx=c and a+b=2.
if the given equation has a solution for all real values of a, then number of integral values of c are?
 

Grade:11

1 Answers

Arnav Prasad
44 Points
8 years ago
Condition for solution is,
|c| equal to, or less than (a2+b2)½.
b = 2 – a. And a = 2 – b.
NOTE : We can say that it has a solution for all real values of b as well.
Putting b = 2 – a.
|c| equal to, or less than (2a2 – 4a + 4)1/2.
Since “a” can be any real value,
Let “a” tend to a very large number.
|c| equal to, or less than (A very large Number).
 
Thus, infinitely many integral values of c.

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