and are two reals such that the sum of their square is equal to 1
Therefore there exists such that
The equation becomes
And since and there are no solution
Given that , show that the equation acosx + bsin x = c has no real roots.
acosx + bsiny = c
as cos(x-y) = c/sqrt(a^2 + b^2)
where cos y = a/sqrt(a^2+b^2) and siny = b/sqrt(a^2 + b^2)
Since a^2 + b^2 < c^2
Hence, no real solution
Could someone please explain to me how the solution works? I'm confused.