Determine the exact value of sin pi4 cos 0 sin pi6 cos pi D

Determine the exact value of sin pi/4 cos 0 - sin pi/6 cos pi Determine the exact value of cos(5 pi/6 + pi/6) + cos(5 pi/6) + cos(pi/6)

Solution

23) sin(pi/4)cos(0) - sin(pi/6)cos(pi)

value of cos0 =1 and cospi = -1

value of sinpi/4 = 1/sqrt2

value of sinpi/6 = 1/2

So, plugging all values : sin(pi/4)cos(0) - sin(pi/6)cos(pi) = 1/sqrt2 + 1/2 = ( 1+sqrt2)/2

24) cos(5pi/6 +pi/6) +cos(5pi/6) +cos(pi/6)

= cos(pi) +cos(pi +pi/6) +cospi/6

{ cospi/6) = sqrt3/2 )

= -1 - sqrt3/2 +sqrt3/2

= - 1