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

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

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0=sin(x)-cos(x)

0 = sin (x) - cos (x)

x = \frac{π}{4} + πn

Degrees

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

Solution steps

0 = sin (x) - cos (x)

Switch sides

sin (x) - cos (x) = 0

Rewrite using trig identities

sin (x) - cos (x) = 0

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

tan (x) - 1 = 0

tan (x) - 1 = 0

Move

1

to the right side

tan (x) - 1 = 0

Add

1

to both sides

tan (x) - 1 + 1 = 0 + 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

1 - tan^{2} (x) = sec^{2} (x)

cos (2 θ - \frac{π}{2}) = - 1, 0 \leq θ < 2 π

sinh (x) = - \frac{3}{4}

tan (3 θ) = 1

7 - 7 sin (θ) = 7

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