Question

Given that sin(x + 60) degree = cos(2x) degree, find tan(x + 60) degree.

Answer 1

well,
tan(x+60) = sin(x+60)/cos(x+60)
= cos(2x)/cos(x+60)

sin(x+60)-cos(2x) = 0
cos(30-x)-cos(2x) = 0
using the sum-to-product formulas,
2sin(x/2 + 15)sin(3x/2 + 15) = 0
set each factor to 0 to find values of x that make it zero.
Then take tan(x+60)

Answer 2

Cos = sin(90 - 2x)
Sin(x + 60) = sin(90 - 2x)
x + 60 = 90 - 2 x
3x + 60 = 90
3x = 30
x = 10
Tan(x + 60)
tan(10 + 60)
tan(70)
= 2.747

Answer 3

boy - how did I miss that solution?
of course, there are probably solutions in other quadrants, since sin(180-x) = sin(x)

Answer 4

not understood

Answer 5

Iam not understanding