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

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

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cos(x+pi)=sin(x)

cos (x + π) = sin (x)

x = \frac{3 π}{4} + πn

Solution steps

cos (x + π) = sin (x)

Rewrite using trig identities

- cos (x) = sin (x)

Subtract

sin (x)

from both sides

- 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{3 π}{4} + πn

2 cos^{2} (θ) tan (θ) - tan (θ) = 0

3 - 3 sin (x) - 2 cos^{2} (x) = 0

7 cos^{2} (θ) + 11 cos (θ) = cos (θ) - 3

cos^{2} (x) - 9 cos (x) - 1 = 0

3 tan (x) = 2 sin (x)

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