Question

A sin theta + B cos theta what is its maximum and minimum value ​

Answer 1

Answer:

hope you get the problem

Answer 2

It's maximum value is √(a²+b²) and minimum value is √(a²-b²).

• "asinθ + bcosθ" is lie between it's maximum and minimum value as

√(a²-b²) ≤ asinθ + bcosθ ≤ √(a²+b²)

• let y = asinθ + bcosθ

=dy/dx = acosθ - bsinθ = 0 for max/min

=bsinθ = acosθ

=sinθ/cosθ = a/b

=tanθ = a/b

then the hypotenuse of the corresponding right-angled triangle is √(a² + b²)  

• the max/min of y occurs when tanθ = a/b

then sinθ= a/√(a² + b²) and cosθ = b/√(a² + b²)

• y = a( a/√(a² + b²)) + b( b/√(a² + b²))

= (a² + b²)/√(a² + b²)

= √(a² + b²)