The-value-of-x-between-0-and-2pi-which-satisfy-the-equation-sin-x-8-cos-2-x-1-are-in-AP-Find-the-common-difference-

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}