Question

If A + B = 90° , find the maximum value of sinA×sinB ?

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Answer 1

Step-by-step explanation:

heya..

here is ur answer

sin(b) = sin(90-a) = cos(a), using a trig identity

f(a) = sin(a)*cos(a)

This function is a maximum where df/da = 0

df/da = cos^2(a) - sin^2(a) = 0 -> cos(a) = sin(a) -> tan(a) = 1

The angle whose tangent = 1 is 45 deg.

So the maximum value of sin(a)sin(b) = sin(45)sin(45) = 1/2 

i hope its help u

Answer 2

Answer:

The maximum value of sinA×sinB is 1/2.

✔️Hope it will be helpful.✔️