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

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

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

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

x = \frac{3 π}{4} + πn

Solution steps

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

Rewrite using trig identities

tan (x) + 1 = 0

Move

1

to the right side

tan (x) = - 1

General solutions for

tan (x) = - 1

x = \frac{3 π}{4} + πn

tan^{2} (θ) = 1 - sec^{2} (θ)

x, sin (4 x) = 0

cot (θ) = - \frac{7}{8}

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

α, sin^{2} (α) + sin^{2} (β) = 1

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