Question

Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1. cos 165°

Answer 1

sin(A+B) = sin(A)cos(B)+cos(A)sin(B)
tan(A+B) = [tan(A)+tan(B)]/[1-tan(A)tan(B)]

sin(45degree) = 1/[2^(1/2)] = [2^(1/2)]/2
cos(45degree) = 1/[2^(1/2)] = [2^(1/2)]/2
tan(45degree) = 1
sin(120degree) = [3^(1/2)]/2
cos(120degree) = -1/2
tan(120degree) = -[3^(1/2)]

sin(165) = sin(45+120) = sin(45)cos(120)+cos(45)sin(120)
sin(165) = [2^(1/2)]/2*(-1/2) + [2^(1/2)]/2*[3^(1/2)]/2 = -[2^(1/2)]/4+[3^(1/2)]/4
sin(165) = [sqrt(3)-sqrt(2)]/4

tan(165) =
tan(45+120) = [tan(45)+tan(120)/[1-tan(45)tan(120)]
tan(165) = [1+(-3^(1/2)]/[1-1[-3^(1/2)]
tan(165) = (1-sqrt(3))/(1+sqrt(3))

Answer 2

do this help

Answer 3

No

Answer 4

): sorry

Answer 5

Help please