Question

Tentukan himpunan penyelesaian persamaan

Cos ( x + 75 ) - cos ( x - 15 ) = 0 dengan 0 < x < 360

Answer 1

Verified answer

Note :
-2 sin(a) . cos(b) = cos(a+b) - cos(a-b)

a + b = x + 75
a - b = x - 15
------------------- (+)
2a = 2x + 60
a = x + 30
b = 45
===================================================

cos(x + 75) - cos (x - 15) = 0
-2 sin(x+30) . sin(45) = 0
sin(x+30) = 0
sinx . cos30 + cosx . sin30 = 0
√3 / 2 sinx + 1/2 . cosx = 0
√3. sinx + cosx = 0
√3. sinx = - cosx
sinx / cosx = -1/√3
tanx = -1/√3
x = 150°   ∨    x = 330°