中四附加數學

a)
6tan^2 A-4sin^2 A=1
6sin^2 A - 4sin^2 A cos^2 A = cos^2 A
6sin^2 A - 4sin^2 A ( 1-sin^2 A) = 1-sin^2 A
6sin^2 A - 4sin^2 A + 4sin^4 A = 1-sin^2 A
4sin^4 A+3sin^2 A-1=0
(4sin^2 A-1)(sin^2 A+1)=0
sin^2 A = 1/4 or sin^2 A= -1 (rej) ( ∵ 1 ≧ sin^2 A ≧ 0 )
sinA=1/2
A=30+360n or 150+360n

b)
3sin^2 A - 16sin^2 A cos^2 A + 3cos^2 A =0
3sin^2 A - 16sin^2 A(1-sin^2 A) + 3(1-sin^2 A)=0
3sin^2 A - 16sin^2 A + 16sin^4 A +3 - 3sin^2 A=0
16sin^4 A - 16sin^2 A +3=0
sin^2 A = 3/4 or sinA=1/4
sinA= √3/2 or sinA=1/2
A=60+360n or 120+360n or A=30+360n or 150+360n

2007-11-22 22:10:33 補充：
其實 (a) 跟 (b) 的做法相同,如果明白了方法,應該可以應付大部份 tan 及 sin/cos 的題目.如對題目還有疑問,可以send message給我!