✔ 最佳答案
1(a)(i)
cos^2 1° + cos^2 89°
= cos^2 1° + cos^2 (90°-1°)
= cos^2 1° + sin^2 1°
= 1
1(a)(ii)
cos^2 2° + cos^2 88°
= cos^2 2° + cos^2 (90°-2°)
= cos^2 2° + sin^2 2°
= 1
1(b)
cos^2 1° + cos^2 2° + ...... + cos^2 88° + cos^2 89°
= (cos^2 1° + cos^2 89°) + (cos^2 2° + cos^2 88°) + ... + cos^2 45°
= 44.5
1(c)
sin^2 1°+sin^2 2°+ ...... + sin^2 88° + sin^2 89°
= cos^2 89° + cos^2 88° + ...... + cos^2 2° + cos^2 1°
= 44.5
2(a)
( 1 - u )^2 = 1 - 2u + u^2
2(b)
√( √(81-162cos^2 x + 81 cos^4 x) )
= √( √(9 - 9cos^2 x)^2 )
= √(9 - 9cos^2 x)
2011-06-08 17:35:00 補充：
2(b) 要加一行 !
√[ √(81-162cos^2 x + 81 cos^4 x) ]
= √[ √( 9^2 - 2(9)(9cos^2 x) + (9cos^2 x)^2 ) ]
= √[ √( 9 - 9cos^2 x)^2 ]
= √(9 - 9cos^2 x)
2011-06-12 19:15:29 補充：
2(b) 仲有得做 !
√[ √(81-162cos^2 x + 81 cos^4 x) ]
= √[ √( 9^2 - 2(9)(9cos^2 x) + (9cos^2 x)^2 ) ]
= √[ √( 9 - 9cos^2 x)^2 ]
= √(9 - 9cos^2 x)
= √[ 9( 1 - cos^2 x) ]
= √( 9 sin^2 x )
= +3sin x or -3sin x
