✔ 最佳答案
1. tan60 係special angels 中三應該要背的
tan60 =√3
so √ 3 = 2/x
x = 2 / √3
x= 2√3 / 3 <-分子分母皆乖√3所得
2.
( 1/sin x - sin x ) X 1 /cos x
= 1/(sinx.cos x) - sinx/cosx
= 1/(sinx.sinx/tanx)-tanx [cosx = sinx /tanx , sinx/cosx = tanx]
=1/(sin² x/ 3/2 ) -3/2
= 3/2 sin² x-3/2
=3/2 (sin² x-1)
Since tanx =3/2, and you didn't specify the quadrant of x,
sinx = ± 3/(√(3² +2² )) = ±3/√13= ± 3√13/13
Therfore sin² x = ( ± 3√13/13)² = 9.13/169= 9/13
Therfore
3/2 (sin² x-1)
= 3/2 ( 9/13 -1)
= 3/2 ( -4/13)
= -6/13