Amath .....Trigonometric Functions of General Angles

1) 2 sec²x - 3 secx - 2 = 0
(2sec x + 1)(sec x -2 ) = 0
sec x = -1/2 or sec x =2
cox x = -2 (rej)or cos x = 1/2
cos x = 1/2
x = 360n∘±60∘

2) 2 sin x cos x - sin x +2cos x - 1 = 0
sin x(2cos x - 1) + 2 cos x - 1 = 0
(2 cos x - 1)(sin x + 1) = 0
cos x = 1/2 or sin x = -1
x = 360n∘±60∘or x = 180n∘+(-1)^n 270∘

3) 3 cot² x + (3+√3) cot x + √3 = 0
(3 cot x + 1)(cot x + √3) = 0
cot x = -1/3 or cot x = √3
tan x = -3 or tan x = 1/√3
x = 180n∘- 71.57∘or x = 180n∘+30∘

4) sin^4 x - cos^4 x = cos x
(sin²x + cos²x)(sin²x - cos²x) = cos x
1(sin²x - cos²x) = cos x
- cos²x - cos x + sin²x = 0
cos²x + cos x - sin²x = 0
cos²x + cos x - (1-cos²x) = 0
2cos²x + cos x - 1 = 0
(cos x +1)(2cos x -1) = 0
cos x = -1 or cos x = 1/2
x = 360n∘±180∘or x = 360n∘±60∘

建議發問者把問題分開幾次來問. 這使發問者的分數負擔最少, 也使答案更快獲得. 回答者也有更多機會回答.

1) (2sec x + 1)(sec x -2 ) =
sec x = -1/2 or sec x =2
1/cos x = -1/2 or 1/ cos x = 2
cox x = -2 or cos x = 1/2
x = 60