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...

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.