Use an Addition or Subtraction Formula to write the expressi

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. sin(14 degree) cos(46 degree) + cos(14 degree) sin(46 degree) Find its exact value. Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. cos(4 pi/7) cos(5 pi/21) + sin(4 pi/7) sin(5 pi/21) Find its exact value.

Solution

1) sin (14) cos (46 ) + cos (14 ) sin (46)

applying sin (a+b) rule

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

sin ( 14 + 46 ) = sin (14) cos (46 ) + cos (14 ) sin (46)

= sin (60)

exact value is = sqrt 3/2

2) cos ( 4pi/7 ) cos (5pi/21) + sin (4pi/7) sin (5pi/21)

applying cos ( a- b) formula

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

cos ( 4pi/7 - 5pi/21) = cos ( 4pi/7 ) cos (5pi/21) + sin (4pi/7) sin (5pi/21)

= cos ( 7pi/21)

= cos (pi/3)

exact value is = 1/2