SOLUTION: If a+b = 90degree, Find max value of (sin a.sin b)

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Question 639116: If a+b = 90degree, Find max value of (sin a.sin b)
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
a+b = 90°
  b = 90°-a


sin(a)sin(b) = sin(a)sin(90°-a) = sin(a)cos(a)

We use the identity sin(2a) = 2sin(a)cos(a) by dividing both sides by 2

                    sin%282a%29%2F2 = sin(a)cos(a)

So

sin(a)sin(b) = sin(a)sin(90°-a) = sin(a)cos(a) = sin%282a%29%2F2   

The maximum value of the sine function is 1

so the maximum value of sin%282a%29%2F2 is 1%2F2

Answer: 1%2F2

Edwin