數學題目 三角比 ! ( 20點 )

√sin^2 60-cos^2 60)sin30------?

係咪呢個(sin^2 60-cos^2 60)sin30

2009-03-08 00:13:09 補充：
2. tan60-tan30/1+tan60tan30
=tan(60-30) { tan(A-B)= tanA-tanB/1+tanAtanB }
=tan30
=開方3/3

3. 已知cos theta=√3/2和tan theta=1/√3,利用三角恆等式,搵sin theta的值
(吾知點做,但我知答案係 1/2)



4. 已知cos theta =0.1 搵1+ sin theta tan theta / cos theta 的值

cos theta =0.1
theta=84.3

1+ sin theta tan theta / cos theta
=1+ sin 84.3 tan 84.3 / cos 84.3
=109



5. 已知tan theta =2 搵 3sin theta - 4cos theta/3sin theta + 4cos theta 的值
tan theta=2
theta=63.4

Hence, 3sin 63.4 - 4cos 63.4/ 3sin63.4 + 4cos 63.4=0.2


6. sin^3 theta+cos^2 theta sin theta -sin theta
=sin theta (sin^2 theta + cos^2 theta -1)
=sin theat (1 - 1)
=0

7. cos theta sin theta (1/tan^2 theta +1)
= cos theta sin theta { (cos^2 theta /sin^2 theta) +1 }
= cos theta sin theta { (cos^2 theta +sin^2 theta)/sin^2 theta }
= cos theta sin theta ( 1/sin^2 theta)
=cos theta / sin theta
=1/ tan theta
=cot theta ====(吾知你教左未..)

8. 1/1-sin theta + 1/1+ sin theta
={ (1+ sin theta) + (1-sin theta) } / (1-sin theta )( 1+sin theta)
=2/ 1- sin^2theta
=2/ cos theta






10. tan theta + 1/tan(90-theta) { 1/tan(90-theta) = tan theta }
=tan theta+tan theta
=2tan theta


11. 4/tan(90- theta) - sin theta / sin(90-theta)
=4tan theta - sin theta /costheta
=4tan theta -tan theta
=3tan theta





13.cos^4 theta -sin^4 theta
=(cos^2theta)^2 - (sin^2theta)^2
=(cos^2theta + sin^2theta) (cos^2theta - sin^2theta)
=(1) (cos^2theta - sin^2theta)
=- (sin^2theta + cos^2theta)
= -1

2009-03-08 00:15:31 補充：
其他果D,有D吾識計+時間不早,我要訓教...做到呢到...