Use a sum or difference formula to find the exact value of t

Use a sum or difference formula to find the exact value of the following. sin 4 pi/5 cos pi/30 + cos 4 pi/5 sin pi/30

sin 4pi/5 cos pi/30 + cos 4pi/5 sin pi/30

appying sin (a+b) formula

sin (a+b) = sin a cos b + cos a sin b

comparing the expression with the formula

a = 4pi/5

b = pi/30

hence,

sin 4pi/5 cos pi/30 + cos 4pi/5 sin pi/30 = sin ( 4pi/5 + pi/30 )

= sin ( 25pi/30) = sin ( 5pi/6) = 1/2