MATHS F.4 THX!!!

2010-07-02 10:02 pm

1.If tan x =3,then sin^2 X / 1+cos^2 X = ?

ANS is 9/11

2.sin^2 (180+x)-cos(180+X)cos(-X)+1

ANS is 2

P.S. (180+x) =180度+X

3.Let f(X)=(X-1)^2.If f(X) is divisible by X+K

Find the remainder when f(X) is divided by X-K

ANS is 4

THX!!!

回答 (1)

用戶2053

2010-07-02 10:38 pm

✔ 最佳答案

1)
sin^2 X / 1+cos^2 X
= (sin^2 X) / [(sin^2 X + cos^2 X) + cos^2 X]
= [(sin^2 X) / (cos^2 X)] / { [(sin^2 X + cos^2 X) + cos^2 X] / (cos^2 X) }
= (tan^2 X) / [ (tan^2 x + 1) + 1 ]
= (3^2) / [ (3^2 + 1) + 1 ]
= 9/11
2)
sin^2 (180+x)-cos(180+X)cos(-X)+1
= ( - sin x)^2 - (- cos x)(cos x) + 1
= (sin x)^2 + (cos x)^2 + 1
= 1 + 1
= 2
3)
By remainder theorem ,
f(-K) = ( - K - 1)^2 = 0
- K - 1 = 0
K = - 1
When f(X) is divided by X-K ,
By remainder theorem ,
the remainder
= f(K)
= f(- 1)
= ( - 1 - 1)^2
= (-2)^2
= 4

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