Buktikanlah :
a) Sin3A = 3 Sin A - 4 Sin³ A
b) Cos4A = 8Cos^4A-8Cos²A+1
a) Sin3A = 3 Sin A - 4 Sin³ A
b) Cos4A = 8Cos^4A-8Cos²A+1
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a) sin 3A
= sin (2A + A)
= sin 2A . cos A + cos 2A . sin A
= 2 sin A cos A . cos A + (1 - 2 sin² A) . sin A
= 2 sin A . cos² A + sin A - 2 sin³ A
= 2 sin A (1 - sin² A) + sin A - 2 sin³ A
= 2 sin A - 2 sin³ A + sin A - 2 sin³ A
= 2 sin A + sin A - 2 sin³ A - 2 sin³ A
= 3 sin A - 4 sin³ A
(terbukti)
b) cos 4A
= cos (2 . 2A)
= cos² 2A - sin² 2A
= cos² 2A - (1 - cos² 2A)
= cos² 2A - 1 + cos² 2A
= cos² 2A + cos² 2A - 1
= 2 cos² 2A - 1
= 2 (2 cos² A - 1)² - 1
= 2 (4 cos^4 A - 4 cos² A + 1) - 1
= 8 cos^4 A - 8 cos² A + 2 - 1
= 8 cos^4 A - 8 cos² A + 1
(terbukti)