Question

Sin x +√3 coax= √2
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Answer 1

The two values of x are 2n*pi + pi/12 and 2n*pi -5pi/12

Step-by-step explanation:

The given equation is

Sin x +√3 Cosx= √2

Upon dividing the equation by 2 we get

`(1)/(2)Sinx + (√(3) )/(2)Cosx = (√(2) )/(2)`

Sin(
`(pi)/(6)`)*Sinx + Cos(
`(pi)/(6)`)*Cosx =
`(1)/(√(2) )`

This makes the formula of

CosACosB + SinASinB = Cos(A-B)

Cos(x-
`(pi)/(6)`) =
`(1)/(√(2) )`

cos(x- pi/6) = cos(pi/4)

upon writing the general equation we get

x-pi/6 = 2n*pi ± pi/4

x = 2n*pi ± pi/4 -pi/6

so we will have two solutions

x = 2n*pi + pi/4 -pi/6

= 2n*pi + pi/12

and

x = 2n*pi - pi/4 -pi/6

= 2n*pi -5pi/12

Therefore the two values of x are 2n*pi + pi/12 and 2n*pi -5pi/12.