use an addition or subtraction formula to find the exact val

use an addition or subtraction formula to find the exact value

a) sin (15°)

Solution

a) sin (-15)

applying sin (A - B ) formula

sin (-15) = sin (30 - 45 )

sin ( 30 - 45 ) = sin 30 cos 45 - cos 30 sin 45

= 1/2 * sqrt 2 / 2 - sqrt 3/2 * sqrt 2 / 2

= sqrt 2 / 4 - sqrt 6 / 4

sin (-15) = ( sqrt 2 - sqrt 6 ) / 4

b) cos 35pi/18 cos 5pi/18 + sin 35pi/18 sin 5pi/18

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

cos ( 35pi / 18 - 5pi/18 ) = cos ( 30pi/18 )

cos ( 5pi/3 ) = 1/2