Question

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

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

Answer 1

Note that
sin(x + y) = sin(x) cos(y) + cos(x) sin(y).

Therefore by setting x = π/2 and y = π/7, obtain
sin(π/2 + π/7) = sin(π/2)*cos(π/7) + cos(π/2)*sin(π/7)

The right side is what we want to evaluate. It is equal to
sin(π/2 + π/7) = sin (9/14)π

Answer:
`sin( (9 \pi )/(14))`