已知角a的终边过P(x,负根号2)(x不等于0),且cosa=根号3比6再乘x.求sina+1/sina的值?

问题描述:

已知角a的终边过P(x,负根号2)(x不等于0),且cosa=根号3比6再乘x.求sina+1/sina的值?

k=-√2/x
cosa=x/√(2+x^2)=√3x/6
1/(2+x^2)=3/36
6+3x^2=36
x^2+2-12=0
x=√13-1
或者x=-(√13+1)
r=√(x^2+2)=√(16+2√13)=√2(8+√13)
sina=-1/(8+√13)=(√13-8)/51
1/sina=-8-√13
sina+1/sina=-(416+50√13)/51