document.write( "Question 631126: If a+b=90degree, Find the maximum value of sin a.sin b \n" ); document.write( "

Algebra.Com's Answer #397372 by htmentor(1343) $\"\"$ $\"About$

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sin(b) = sin(90-a) = cos(a), using a trig identity
\n" ); document.write( "f(a) = sin(a)*cos(a)
\n" ); document.write( "This function is a maximum where df/da = 0
\n" ); document.write( "df/da = cos^2(a) - sin^2(a) = 0 -> cos(a) = sin(a) -> tan(a) = 1
\n" ); document.write( "The angle whose tangent = 1 is 45 deg.
\n" ); document.write( "So the maximum value of sin(a)sin(b) = sin(45)sin(45) = 1/2 \n" ); document.write( "

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