WISKUNDE
GRAAD 12
NOG OEFENINGE
Identiteite : herleidingsformules.
MATHEMATICS
GRADE 12
MORE EXERCISES
Identities : reduction formulae.
Bewys die volgende identiteite, sonder die
Prove the following identities, without
gebruik van sakrekenaars :
using pocket calculators :
cos 175° ⋅ sin 78°
sin 33° ⋅ tan 115°
─────────────── = 1
─────────────
= −1
cos 348° ⋅ cos 185°
cos 123° ⋅ tan 295°
3 tan 65° ⋅ sin 200° ⋅ cos 335°
3
3.
────────────────────── = − ──────
4 sin 160° ⋅ cos 25° ⋅ sin 115°
4 sin 25°
tan 480° ⋅ sin 300° ⋅ cos 14° ⋅ sin (−135°)
3
4.
──────────────────────────── = ──
sin 104° ⋅ cos 225°
2
cos (270° + α) ⋅ tan (180° + α)
5.
───────────────────── = tan2 α
sin (90° − α)
sin (180° − θ) ⋅ sin (90° − θ) ⋅ tan (180° − θ) ⋅ cos (− θ)
6.
──────────────────────────────────── = cos θ
cos (90° + θ) ⋅ cos (θ − 360°) ⋅ tan (−θ)
1
1
2
7.
───────────── − ──────────── = ──────
sin (180° − θ) − 1
cos (90° − θ) + 1
cos2 θ
tan (180° + x) ⋅ cos (360° − x)
8.
───────────────────────────────────── = − sin x
sin (180° − x) ⋅ cos (90° + x) + cos (540° + x) ⋅ cos (− x)
sin 190° ⋅ cos 225° ⋅ tan 390°
1
9.
───────────────────── = − ──
cos 100° ⋅ sin 135°
√3