Question 639116
<pre>
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(2a)/2}}} = sin(a)cos(a)

So

sin(a)sin(b) = sin(a)sin(90°-a) = sin(a)cos(a) = {{{sin(2a)/2}}}   

The maximum value of the sine function is 1

so the maximum value of {{{sin(2a)/2}}} is {{{1/2}}}

Answer: {{{1/2}}}

Edwin</pre>