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

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

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sqrt(2)-cos(x)=sqrt(2)+sin(x)

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

x = \frac{3 π}{4} + πn

Solution steps

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

Subtract

2 + sin (x)

from both sides

- cos (x) - sin (x) = 0

Rewrite using trig identities

- 1 - tan (x) = 0

Move

1

to the right side

- tan (x) = 1

Divide both sides by

- 1

tan (x) = - 1

General solutions for

tan (x) = - 1

x = \frac{3 π}{4} + πn

4 cos^{4} (x) - 2 cos^{3} (x) - 4 cos^{2} (x) + cos (x) + 1 = 0

112 = 72 + 40 cos (18 t)

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

cos (2 x) = - 0.32

sin (\frac{3 π}{2} - 0) = - cos (x)

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