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

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

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

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

x = \frac{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

Divide both sides by

- 1

tan (x) = 1

General solutions for

tan (x) = 1

x = \frac{π}{4} + πn

sin (3 θ) = \frac{1}{2}

- sin^{2} (θ) + cos^{2} (θ) = 1 - sin (θ)

1 - sin (θ) = 2 cos^{2} (θ)

2 sin^{2} (θ) - 3 sin (θ) = 0

sec^{2} (x) + 2 tan (x) = 4

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