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

Solution steps

0 = cos (x) + sin (x)

Switch sides

cos (x) + sin (x) = 0

Rewrite using trig identities

1 + tan (x) = 0

Move

1

to the right side

tan (x) = - 1

General solutions for

tan (x) = - 1

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