Write the expression as either the sine, cosine, or tangent of a single angle.

cosine of pi divided by five times cosine of pi divided by seven plus sine of pi divided by five times sine of pi divided by seven.

The expression is:

cos (π / 5) cos (π/7) + sin (π/5) sin (π/7)

This expression can be reduced into a trigonometric function with one angle if we make use of the trigonometric identities. The appropriate identity is:

cos (A - B) = cos A cos B + sin A sin B

If we let

A = π / 5

B = π / 7

Therefore,

cos (π / 5) cos (π/7) + sin (π/5) sin (π/7) = cos (π/5 - π/7) = cos (2π/35)

The answer is cos (2pi/35)