What is the general solution for cos(45+x)-cos(45-x)=sqrt(2)cos(x) ?

The general solution for cos(45+x)-cos(45-x)=sqrt(2)cos(x) is x=135+180n

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cos(45+x)-cos(45-x)=sqrt(2)cos(x)

cos (4 5^{\circ} + x) - cos (4 5^{\circ} - x) = 2 cos (x)

x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

cos (4 5^{\circ} + x) - cos (4 5^{\circ} - x) = 2 cos (x)

Rewrite using trig identities

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

Subtract

2 cos (x)

from both sides

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

Rewrite using trig identities

- 2 tan (x) - 2 = 0

Move

2

to the right side

- 2 tan (x) = 2

Divide both sides by

- 2

tan (x) = - 1

General solutions for

tan (x) = - 1

x = 13 5^{\circ} + 18 0^{\circ} n

sin (b) = cos (2 b - 30)

2 sin (x) cos (x) - 4 cos (x) - sin (x) + 2 = 0

\frac{sin ( \frac{π}{2} )}{5} = \frac{sin ( x )}{4}

cos (3 x - 1) = \frac{1}{2}

tan^{2} (x) = sec (x) + 1

What is the general solution for cos(45+x)-cos(45-x)=sqrt(2)cos(x) ?
The general solution for cos(45+x)-cos(45-x)=sqrt(2)cos(x) is x=135+180n