Question 305319
if a+b=90degree, then the maximum value of cosacosb is..
<pre><b>
Let a = x, since the letters x is usually a variable, and 
letters a and b are usually constants.  Then b = 90°-a = 90°-x 

I will approach it from a calculus standpoint.


y = cos(x)cos(90-x)

y = cos(x)sin(x)

{{{(dy)/(dx) = cos(x)cos(x) + sin(x)(-sin(x))

{{{(dy)/(dx) = Cos^2x - Sin^2x}}}

{{{(dy)/(dx) = Cos(2x)}}}

Setting that = 0

Cos(2x)=0

2x = 90°, 270°, 450°, etc.

x = 45°, 135°, 225°, etc.

Substituting these in 

y = cos(x)sin(x)

y = cos(45°)sin(45°) = {{{(sqrt(2)/2)*(sqrt(2)/2)=2/4 = 1/2}}}

y = cos(135°)sin(135°) = {{{(-sqrt(2)/2)*(sqrt(2)/2)=-2/4 = -1/2}}}

y = cos(225°)sin(225°) = {{{(-sqrt(2)/2)*(-sqrt(2)/2)=2/4 = 1/2}}}

etc.

So the maximum value is {{{1/2}}} and the minimum value is {{{-1/2}}}.

Edwin</pre>