What is the general solution for sin(x+pi/4)+sin(x+pi/4)=-1 ?

The general solution for sin(x+pi/4)+sin(x+pi/4)=-1 is x=2pin+(11pi)/(12),x=2pin+(19pi)/(12)

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sin(x+pi/4)+sin(x+pi/4)=-1

sin (x + \frac{π}{4}) + sin (x + \frac{π}{4}) = - 1

x = 2 πn + \frac{11 π}{12}, x = 2 πn + \frac{19 π}{12}

Solution steps

sin (x + \frac{π}{4}) + sin (x + \frac{π}{4}) = - 1

Simplify

sin (x + \frac{π}{4}) + sin (x + \frac{π}{4}) : 2 sin (x + \frac{π}{4})

2 sin (x + \frac{π}{4}) = - 1

Divide both sides by

2

sin (x + \frac{π}{4}) = - \frac{1}{2}

General solutions for

sin (x + \frac{π}{4}) = - \frac{1}{2}

x + \frac{π}{4} = \frac{7 π}{6} + 2 πn, x + \frac{π}{4} = \frac{11 π}{6} + 2 πn

Solve

x + \frac{π}{4} = \frac{7 π}{6} + 2 πn : x = 2 πn + \frac{11 π}{12}

Solve

x + \frac{π}{4} = \frac{11 π}{6} + 2 πn : x = 2 πn + \frac{19 π}{12}

x = 2 πn + \frac{11 π}{12}, x = 2 πn + \frac{19 π}{12}

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

4 sin^{2} (x) + 9 = 12

tan (- 60 s) = - tan (6 0^{\circ})

3 cos^{2} (x) - 5 cos (x) - 2 = 0, (0^{\circ}, 36 0^{\circ})

3 - 5 cos (x) = 0

What is the general solution for sin(x+pi/4)+sin(x+pi/4)=-1 ?
The general solution for sin(x+pi/4)+sin(x+pi/4)=-1 is x=2pin+(11pi)/(12),x=2pin+(19pi)/(12)