✔ 最佳答案
tan(30+x) tan(30-x) = 1-2cos2x
[(tan30+tanx)/(1-tan30tanx)][(tan30-tanx)/(1+tan30tanx)]= 1-2cos2x
[(1/√3+tanx)/(1-(1/√3)tanx)][(1/√3-tanx)/(1+(1/√3)tanx)]= 1-2cos2x
[(1+√3tanx)/(√3-tanx)][(1-√3tanx)/(√3+tanx)]= 1-2cos2x
(1-3tan^2x)/(3-tan^2x)= 1-2cos2x
(1-3tan^2x)=(3-tan^2x)( 1-2cos2x)
(1-3sin^2x/cos^2x)=(3-sin^2x/cos^2x)(1-4cos^2x+2)
(cos^2x-3sin^2x)=(3cos^2x-sin^2x)(3-4cos^2x)
(cos^2x-3sin^2x)=(3-3sin^2x-sin^2x)(4sin^2x-1)
(1-4sin^2x)=(3-4sin^2x)(4sin^2x-1)
(1-4sin^2x)=-16sin^4x+16sin^2x-3
16sin^4x-20sin^2x+4=0
4sin^4x-5sin^2x+1=0
(4sinx-1)(sinx-1)=0
sin^2x=1/4 or sin^2x=1
when sin^2x=1/4
sinx=1/2 or -1/2
x=180π+(-1)^n(30) or 180π+(-1)^n(-30)
when sin^2x=1
sinx=1 or -1
x=180π+(-1)^n(90) or 180π+(-1)^n(-90)
x=180π+(-1)^n(90)