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

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

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sin(x+pi)+cos(x+pi)=0

sin (x + π) + cos (x + π) = 0

x = \frac{3 π}{4} + πn

Degrees

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

Solution steps

sin (x + π) + cos (x + π) = 0

Rewrite using trig identities

sin (x + π) + cos (x + π) = 0

Divide both sides by

cos (x + π), cos (x + π) \neq = 0

\frac{sin ( x + π ) + cos ( x + π )}{cos ( x + π )} = \frac{0}{cos ( x + π )}

Simplify

\frac{sin ( x + π )}{cos ( x + π )} + 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

Subtract

1

from 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{3 π}{4} + πn

x = \frac{3 π}{4} + πn

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