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

The general solution for 0=cos(x)+sin(x) is x=(3pi)/4+pin

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0=cos(x)+sin(x)

0 = cos (x) + sin (x)

x = \frac{3 π}{4} + πn

Degrees

x = 13 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

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

1 - 2 sin (x) = 0

tan (\frac{x}{2} - \frac{π}{2}) = 2

8 sec (x) + 8 tan (x) = 8

25 cot^{2} (θ) - 16 = 0

2 sin^{2} (x) = sin (x) + 1

What is the general solution for 0=cos(x)+sin(x) ?
The general solution for 0=cos(x)+sin(x) is x=(3pi)/4+pin