What is the general solution for sin^2(x)+cos^2(x)-1+cos(x)-sin(x)=0 ?

The general solution for sin^2(x)+cos^2(x)-1+cos(x)-sin(x)=0 is x= pi/4+pin

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sin^2(x)+cos^2(x)-1+cos(x)-sin(x)=0

sin^{2} (x) + cos^{2} (x) - 1 + cos (x) - sin (x) = 0

x = \frac{π}{4} + πn

Solution steps

sin^{2} (x) + cos^{2} (x) - 1 + cos (x) - sin (x) = 0

Rewrite using trig identities

1 - tan (x) = 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 (4 x) - cos (2 x) = 0

\frac{6}{π} = 3 cos (2 x)

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

4 - 8 cos^{2} (x) = 0

cos^{2} (x) = \frac{1 - cos ( 2 x )}{2}

What is the general solution for sin^2(x)+cos^2(x)-1+cos(x)-sin(x)=0 ?
The general solution for sin^2(x)+cos^2(x)-1+cos(x)-sin(x)=0 is x= pi/4+pin