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

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

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0=sin(x)+cos(x)

0 = sin (x) + cos (x)

x = \frac{3 π}{4} + πn

Solution steps

0 = sin (x) + cos (x)

Switch sides

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

sec (x) tan (x) = 2

cos (x) = cot (x)

4 cos (x) - 2 = 0

4 sin (x) = sec (x)

tan^{2} (x) = \frac{1}{2}

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