find the expression as the cosine of an angle>> cos (pi/5)cos pi/3-sin(pi/5)sin pi/3

Hello!
It is a relatively simple task. The only formula we need to solve this is the formula of cosine of a sum of two angles:
cos( u + v ) = cos( u ) * cos( v ) - sin( u )*sin( v ).
This formula is true for any real numbers u, v. We shall use it in the reverse direction:
cos( u ) * cos( v ) - sin( u )*sin( v ) = cos( u + v ).
In our case we have u = pi / 5, v = pi / 3 (or vice versa). From the above formula we obtain
cos( pi / 5 ) * cos( pi / 3 ) - sin( pi / 5 )*sin( pi / 3 ) = cos( pi / 5 + pi / 3 ),
which is clearly equal to cos( 8/15 pi ). It is the answer.
https://www.purplemath.com/modules/idents.htm

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