prove that sin 3b + (cos b+sin b)(1−2sin 2b) = cos 3b


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Question Number 84469 by jagoll last updated on 13/Mar/20

$prove that$ $\sin 3 b + (\cos b + \sin b) (1 - 2 \sin 2 b)$ $= \cos 3 b$
	Answered by som(math1967) last updated on 13/Mar/20

	$s i n 3 b + c o s b - 2 s i n 2 b c o s b + \sin b - 2 \sin b \sin 2 b$ $= s i n 3 b + c o s b - (s i n 3 b + s i n b)$ $+ s i n b - (c o s b - c o s 3 b) ★$ $= c o s 3 b$ $★ 2 s i n A c o s B = s i n (A + B) + s i n (A - B)$ $2 s i n A s i n B = c o s (A - B) - \cos (A + B)$
	Commented by jagoll last updated on 13/Mar/20

	$thank you . but typo sir$ $2 \sin Asin B = \cos (A - B) - \cos (A + B)$
	Commented by som(math1967) last updated on 13/Mar/20

	$y e s i f i x i t$
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