Maths Summer Homework 15pt.

(a) (tan^2 30° * sin^2 45°)/cos^2 60°
= [1/rt(3)^2 x 1/rt(2)^2] / (1/2)^2
= (1/3 x 1/2) / 1/4
= 2/3

b) sin^2 45° - cos^2 45° + sin 30° *cos 60° + tan 60°
=1/rt(2)^2 - 1/rt(2)^2 + 1/2*1/2 + rt(3)
=1/4 + rt(3)

3a) (tan^2 30° * sin^2 45°)/cos^2 60°
= (1/root3)^2 * (1/root2)^2 / (1/2)
= (1/3) * (1/2) * 2
= 1/3

b) sin^2 45° - cos^2 45° + sin 30° *cos 60° + tan 60°
= (1/root2)^2 - (1/root2)^2 + (1/2)(1/2) + root3
= 1/2 - 1/2 + 1/4 + root3
= 1/4 + root3

p.s. root = 平方根

3a ((1/sqrt(3))^2 * (1/sqrt(2))^2)/(1/2)^2
= (1/3 * 1/2)/(1/4)
= 2/3

b sqrt(2)^2 - sqrt(2)^2 + (1/2)(1/2) + sqrt(3)
= 2 - 2 + 1/4 + sqrt(3)
= 1/4+ sqrt(3)

(tan^2 30° * sin^2 45°)/cos^2 60°
= (1/3)(1/2) / (1/4)
= 2/3
-----------------------------------------------------
sin^2 45° - cos^2 45° + sin 30° *cos 60° + tan 60°
= 1/2 - 1/2 + (1/2) (1/2) + sqrt(3)
= sqrt(3) + 1/4
-----------------------------------------------------
sqrt(3) = 根 3
sin 45° = cos 45° = 1/sqrt(2)
tan 30° = 1/sqrt(3)
sin 30° = cos 60° = 1/2
tan 60° = sqrt(3)
上面全部都要背

2007-08-28 21:42:22 補充：
慢左, 要寫解釋, 請多多支持