Form 3 Maths 幫幫手 － Q 3

let theta be x

L.H.S = sinxcosx(1+tan^2x)

=sinxcosx[1+sin^2x/cos^2x]

=sinxcosx[(cos^2x+sin^2x)/cos^2x]

=sinxcosx(1/cos^2x) (cos^2x + sin^2x) = 1

=sinx/cosx

=tanx (sinx/cosx = tanx)

=R.H.S

so sinxcosx(1+tan^2x )= tanx is an identity.

2008-02-09 14:56:27 補充：

或許可向MSN問我-v-maths-science_1993314@hotmail.com

2008-02-09 15:04:28 補充：

the details ans :http://hk.geocities.com/doortyui/maths1.jpg

2008-02-10 09:42:10 補充：

樓請注意. 人地先至係F.3如果佢唔係F.3我一早用左條式啦...

其實(1+tan^2θ) 是等於sec^2θ

而sec^2θ=1/(cos^2θ)

所以條問題

sinθcosθ (1+tan^2 θ) = tanθ

LHS:sinθ(cosθ)(1/cos^2θ)

=sinθ/cosθ

=tanθ

RHS=tanθ

so it's an identity

2008-02-09 15:47:51 補充：

有一條formula"1 tan^2θ=sec^2θ"所以先equal...唔知你學左味呢??"

2008-02-09 15:49:06 補充：

sorry..係"1 tan^2θ=sec^2θ"