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

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

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sin(x+pi/4)+sin(x-pi/4)=0

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) = 0

x = 2 πn, x = π + 2 πn

Solution steps

sin (x + \frac{π}{4}) + sin (x - \frac{π}{4}) = 0

Rewrite using trig identities

2 sin (x) = 0

Divide both sides by

2

sin (x) = 0

General solutions for

sin (x) = 0

x = 0 + 2 πn, x = π + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 2 πn, x = π + 2 πn

cos (x) (tan (x) + \frac{cos ( x )}{sin ( x )}) = 2

2 cos (2 x) + sin (x) = \frac{1}{2}

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

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

- 2 + 3 csc (x) = 5

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