Question

Buktikan
sinx − sin3x − sin5x + sin7x = −4sinx sin2x sin4x

Answer 1

Verified answer

Jawab

sin x - sin 3x - sin 5x + sin 7x = - 4 sin x sin 2x sin 4x

sin x -sin 3x - sin 5x + sin 7x =
= (sin 7x + sin x) -( sin 5x + sin 3x)
= 2 sin 1/2 (7x + x) cos 1/2 (7x - x) - ( 2 sin 1/2 (5x+3x) cos 1/2(5x-3x))
= (2 sin 4x cos 3x) -  (2sin 4x cos x)
= 2 sin 4x ( cos 3x - cos x)
= 2 sin 4x ( - 2 sin 1/2(3x+x)  sin 1/2(3x-x))
= 2 sin 4x (- 2 sin 2x sin x)
= - 4 sin x sin 2x sin 4x
terbukti

Answer 2

Verified answer

Trigonometri Analitik.

sin A + sin B = 2 sin [(A + B) / 2] cos [(A - B) / 2]
cos A - cos B = -2 sin [(A + B) / 2] sin [(A - B) / 2]
cos (-θ) = cos θ

sin x - sin 3x - sin 5x + sin 7x
= (sin 7x + sin x) - (sin 3x + sin 5x)
= 2 sin 4x cos 3x - 2 sin 4x cos x
= 2 sin 4x (cos 3x - cos x)
= 2 sin 4x (-2 sin 2x sin x)
= -4 sin x sin 2x sin 4x
TERBUKTI!!!