What is the general solution for solvefor x,0=cos(x)-sin(x) ?

The general solution for solvefor x,0=cos(x)-sin(x) is x= pi/4+pin

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

solve for

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

x = \frac{π}{4} + πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

0 = cos (x) - sin (x)

Switch 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

Subtract

1

from 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{π}{4} + πn

x = \frac{π}{4} + πn

3 cos^{2} (θ) + 7 cos (θ) - 8 = 0

2 cos (2 a) = 2, 0 \leq θ \leq 2 π

t, y^{4} - 81 y = sin (t)

11 sin (B) - 1 = 3 sin (B) - 1

sin (5 x) - sin (3 x) - sin (x) = 0

What is the general solution for solvefor x,0=cos(x)-sin(x) ?
The general solution for solvefor x,0=cos(x)-sin(x) is x= pi/4+pin