The solution to the problem is as follows: let y = asinx + bcosx dy/dx = acosx - bsinx = 0 for max/min bsinx = acosx sinx/cosx = a/b tanx = a/b then the hypotenuse of the corresponding right-angled triangle is √(a^2 + b^2)
the max/min of y occurs when tanx = a/b then sinx = a/√(a^2 + b^2) and cosx = b/√(a^2 + b^2) y = a( a/√(a^2 + b^2)) + b( b/√(a^2 + b^2)) = (a^2 + b^2)/√(a^2 + b^2) = √(a^2 + b^2)
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