What is the general solution for cos(x1)-cos(x2)=cos(x1-x2) ?

The general solution for cos(x1)-cos(x2)=cos(x1-x2) is x= pi/4+pin,x=(3pi)/4+pin

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cos(x1)-cos(x2)=cos(x1-x2)

cos (x 1) - cos (x 2) = cos (x 1 - x 2)

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Solution steps

cos (x \cdot 1) - cos (x \cdot 2) = cos (x \cdot 1 - x \cdot 2)

Rewrite using trig identities

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

Subtract

cos (x) cos (2 x) + sin (x) sin (2 x)

from both sides

cos (x) - cos (2 x) - cos (x) cos (2 x) - sin (x) sin (2 x) = 0

Rewrite using trig identities

- cos (2 x) = 0

Divide both sides by

- 1

cos (2 x) = 0

General solutions for

cos (2 x) = 0

2 x = \frac{π}{2} + 2 πn, 2 x = \frac{3 π}{2} + 2 πn

Solve

2 x = \frac{π}{2} + 2 πn : x = \frac{π}{4} + πn

Solve

2 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{4} + πn

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

8 \cdot sin^{2} (2 x) - 2 \cdot sin (2 x) - 1 = 0

4 - 2 cos (2 x) = 0

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

2 cos^{2} (x) + 6 cos (x) = - 1

8 sin^{2} (x) - 2 cos (x) = 5

What is the general solution for cos(x1)-cos(x2)=cos(x1-x2) ?
The general solution for cos(x1)-cos(x2)=cos(x1-x2) is x= pi/4+pin,x=(3pi)/4+pin