Question

Jika 3 tan x + cot x = 5 csc x dan 0° ≤ x ≤ 360° maka cos x = ...

Answer 1

3 tanx + cot x = 5 cscx
kalikan tanx di kedua ruas

3tan²x + 1 = 5/sinx * (sinx/cosx)
3(sin²x/cos²x) + 1 = 5/cosx
3((1 - cos²x)/cos²x) + 1 = 5/cosx

misal, cosx = a

3(1 - a²)/a² + 1 = 5/a
(3 - 3a²)/a² + a²/a² = 5a/a²
(3 - 3a² + a² - 5a)/a² = 0
(-2a² - 5a + 3)/a² = 0
(a + 3)(-2a + 1)/a² = 0

a + 3 = 0
a = -3
(tidak ada nilai yang memenuhi karena interval cosx, 1 ≤ cosx ≤ -1 )

-2a + 1 = 0
-2a = -1
2a = 1
a = 1/2

cosx = 1/2
x = 60°, 300°