What is the general solution for sin(x+pi)-sin(x)+sqrt(2)=0 ?

The general solution for sin(x+pi)-sin(x)+sqrt(2)=0 is x=2pin-pi/2+(3pi)/4 ,x=2pin-pi/2+(5pi)/4

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sin(x+pi)-sin(x)+sqrt(2)=0

sin (x + π) - sin (x) + 2 = 0

x = 2 πn - \frac{π}{2} + \frac{3 π}{4}, x = 2 πn - \frac{π}{2} + \frac{5 π}{4}

Solution steps

sin (x + π) - sin (x) + 2 = 0

Rewrite using trig identities

2 + 2 cos (\frac{2 x + π}{2}) = 0

Move

2

to the right side

2 cos (\frac{2 x + π}{2}) = - 2

Divide both sides by

2

cos (\frac{2 x + π}{2}) = - \frac{2}{2}

General solutions for

cos (\frac{2 x + π}{2}) = - \frac{2}{2}

\frac{2 x + π}{2} = \frac{3 π}{4} + 2 πn, \frac{2 x + π}{2} = \frac{5 π}{4} + 2 πn

Solve

\frac{2 x + π}{2} = \frac{3 π}{4} + 2 πn : x = 2 πn - \frac{π}{2} + \frac{3 π}{4}

Solve

\frac{2 x + π}{2} = \frac{5 π}{4} + 2 πn : x = 2 πn - \frac{π}{2} + \frac{5 π}{4}

x = 2 πn - \frac{π}{2} + \frac{3 π}{4}, x = 2 πn - \frac{π}{2} + \frac{5 π}{4}

3 tan (x) = - 3

2 (sin (x))^{2} - 5 cos (x) + 1 = 0

5 sin (x) cos (x) = 3 cos (x)

3 cos (x) + sin (x) = 2

9 cosh (x) - 5 sinh (x) = 15

What is the general solution for sin(x+pi)-sin(x)+sqrt(2)=0 ?
The general solution for sin(x+pi)-sin(x)+sqrt(2)=0 is x=2pin-pi/2+(3pi)/4 ,x=2pin-pi/2+(5pi)/4