Respuesta :
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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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)
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
