5.7.5 Fungsi Trigonometri, SPM Praktis (Kertas 1)


5.7.5 Fungsi Trigonometri, SPM Praktis (Kertas 1)

Soalan 11:
Buktikan identiti ko s 2 x 1sinx =1+sinx  

Peneyelesaian:
Sebelah kiri = ko s 2 x 1sinx = 1 sin 2 x 1sinx sin 2 x+ko s 2 x=1 = ( 1+sinx )( 1sinx ) 1sinx =1+sinx = Sebelah kanan  


Soalan 12:
Buktikan identiti sin 2 xko s 2 x= tan 2 x1 tan 2 x+1   

Peneyelesaian:
Sebelah kanan  tan 2 x1 tan 2 x+1 = sin 2 x cos 2 x 1 sin 2 x cos 2 x +1 tanx= sinx cosx = sin 2 x cos 2 x cos 2 x sin 2 x+ cos 2 x cos 2 x = sin 2 x cos 2 x sin 2 x+ cos 2 x = sin 2 x cos 2 x sin 2 x+ cos 2 x=1 =Sebelah kiri


Soalan 13:
Buktikan identiti tan2 θ – sin2 θ = tan2 θ sin2 θ

Peneyelesaian:
Sebelah kiri = tan 2 θ sin 2 θ = sin 2 θ cos 2 θ sin 2 θ = sin 2 θ sin 2 θ cos 2 θ cos 2 θ = sin 2 θ( 1 cos 2 θ ) cos 2 θ = sin 2 θ sin 2 θ cos 2 θ =( sin 2 θ cos 2 θ )( sin 2 θ ) = tan 2 θ sin 2 θ =Sebelah kanan


Soalan 14:
Buktikan identiti kosek2 θ (sek2 θ – tan2 θ) – 1 = kot2 θ

Peneyelesaian:
Sebelah kiri,
kosek2 θ (sek2 θ – tan2 θ) – 1
= kosek2 θ (1) – 1  ← (tan2 θ + 1 = sek2 θ
                                    sek2 θ – tan2 θ  = 1)
= kosek2 θ – 1
= kot2 θ  (1 + kot2 θ = kosek2 θ
                        kosek2 θ – 1 = kot2 θ  )
= Sebelah kanan

0 comments:

Post a Comment