Find all numbers for which every root of 3x=a x+(4-2|a|) ^2x is a root of 3x+ 2x=1+2 x 2x

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

Problem

Find all numbers

a

for which every root of

\sin 3x=a\sin x+(4-2|a|)\sin^2x

is a root of

\sin 3x+\cos 2x=1+2\sin x\cos 2x,

and every root of the latter equation is a root of the former.

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