There exist constants

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

There exist constants a,b,ca, b, c, and dd such that (sin⁡x)7=asin⁡7x+bsin⁡5x+csin⁡3x+dsin⁡x(\sin x)^7 = a \sin 7x + b \sin 5x + c \sin 3x + d \sin x for all angles xx. Find dd.

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