Question 912089
<pre>
cos(75°)cos(30°)+sin(75°)sin(30°) 
(a)
Use the double angle identity:
{{{cos(alpha-beta)=cos(alpha)cos(beta)+sin(alpha)sin(beta)}}}

Observe that the given expression is the right side of this
identity with {{{alpha="75°"}}} and {{{beta="30°"}}}, Substituting

{{{cos("75°-30°") =cos("75°")cos("30°")+sin("75°")sin("30°")}}}

{{{cos("45°") =cos("75°")cos("30°")+sin("75°")sin("30°")}}}

Answer:  cos(45°)

(b) 
Since the exact vaule of cos(45°) is {{{sqrt(2)/2}}},

 cos(75°)cos(30°)+sin(75°)sin(30°) = {{{sqrt(2)/2}}}

Edwin</pre>