SOLUTION: If a+b=90degree, Find the maximum value of sin a.sin b

Question 631126: If a+b=90degree, Find the maximum value of sin a.sin b
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
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
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