The value of x between 0 and 2π which satisfy the equation sin x (√(8 cos^2 x)) = 1 are in AP Find the common difference.


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Question Number 54541 by Tip Top last updated on 05/Feb/19

$The value of x between 0 and 2 π$ $which satisfy the equation$ $\sin x \sqrt{8 \cos^{2} x} = 1 are in AP$ $Find the common difference .$
	Answered by tanmay.chaudhury50@gmail.com last updated on 05/Feb/19

	$s i n x \times (\pm 2 \sqrt{2} c o s x) = 1$ $c o s i d e r i n g + s i g n$ $2 s i n x c o s x = \frac{1}{\sqrt{2}}$ $s i n 2 x = \frac{1}{\sqrt{2}} = s i n (\frac{π}{4}) i n f i r s t q u a d r a n t$ $2 x = \frac{π}{4} \to x = \frac{π}{8}$ $s i n 2 x = \frac{1}{\sqrt{2}} = s i n (π - \frac{π}{4}) \to 2 n d q u a d r a n t$ $2 x = \frac{3 π}{4} \to x = \frac{3 π}{8}$ $n o w c o n s i d e r - s i g n$ $s i n 2 x = - \frac{1}{\sqrt{2}} = s i n (π + \frac{π}{4}) \to 3 r d q u a d r a n t$ $2 x = \frac{5 π}{4} x = \frac{5 π}{8}$ $s i n 2 x = \frac{- 1}{\sqrt{2}} = s i n (2 π - \frac{π}{4})$ $2 x = \frac{7 π}{4} \to x = \frac{7 π}{8}$ $s o v a l u e o f x a r e$ $\frac{π}{8}, \frac{3 π}{8}, \frac{5 π}{8}, \frac{7 π}{8} c o m m o n d i f f e r e n c e = \frac{3 π - π}{8} = \frac{π}{4}$
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