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

Degrees

x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

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

Subtract

2 + sin (x)

from both sides

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

Rewrite using trig identities

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

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{- cos ( x ) - sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

- 1 - \frac{sin ( x )}{cos ( x )} = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

- 1 - tan (x) = 0

- 1 - tan (x) = 0

Move

1

to the right side

- 1 - tan (x) = 0

Add

1

to both sides

- 1 - tan (x) + 1 = 0 + 1

Simplify

- tan (x) = 1

- tan (x) = 1

Divide both sides by

- 1

- tan (x) = 1

Divide both sides by

- 1

\frac{- tan ( x )}{- 1} = \frac{1}{- 1}

Simplify

tan (x) = - 1

tan (x) = - 1

General solutions for

tan (x) = - 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{3 π}{4} + πn

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