find general solution cos (x−45°)=sin (2x+60°)


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Question Number 106220 by bemath last updated on 03/Aug/20

$find general solution \cos (x - 45 °) = \sin (2 x + 60 °)$
	Answered by Dwaipayan Shikari last updated on 03/Aug/20

	$s i n (\frac{π}{2} - x + \frac{π}{4}) = s i n (2 x + \frac{π}{3})$ $\frac{3 π}{4} - x = 2 k π \pm 2 x + \frac{π}{3} (k \in Z)$ $f i r s t c a s e$ $3 x + 2 k π = \frac{5 π}{12}$ $s e c o n d c a s e$ $x = 2 k π + \frac{13 π}{12}$
	Answered by john santu last updated on 03/Aug/20

	Answered by malwaan last updated on 03/Aug/20

	$c o s (x - \frac{π}{4}) = s i n (2 x + \frac{π}{3})$ $s i n (\frac{π}{2} - x + \frac{π}{4}) = s i n (2 x + \frac{π}{3})$ $s i n (\frac{3 π}{4} - x) = s i n (2 x + \frac{π}{3})$ $\frac{3 π}{4} - x = 2 x + \frac{π}{3} + 2 k π$ $\Rightarrow - 3 x = \frac{- 6 π}{12} + 2 k π$ $\Rightarrow x = \frac{π}{6} - \frac{2 π k}{3}$ $o r$ $\frac{3 π}{4} - x = π - (2 x + \frac{π}{3}) + 2 k π$ $\Rightarrow x = 2 k π - \frac{π}{12}$
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