What is the general solution for 2sin(x-pi/2)+sqrt(2)=0 ?

The general solution for 2sin(x-pi/2)+sqrt(2)=0 is x=2pin+(7pi)/4 ,x=2pin+(9pi)/4

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2sin(x-pi/2)+sqrt(2)=0

2 sin (x - \frac{π}{2}) + 2 = 0

x = 2 πn + \frac{7 π}{4}, x = 2 πn + \frac{9 π}{4}

Solution steps

2 sin (x - \frac{π}{2}) + 2 = 0

Move

2

to the right side

2 sin (x - \frac{π}{2}) = - 2

Divide both sides by

2

sin (x - \frac{π}{2}) = - \frac{2}{2}

General solutions for

sin (x - \frac{π}{2}) = - \frac{2}{2}

x - \frac{π}{2} = \frac{5 π}{4} + 2 πn, x - \frac{π}{2} = \frac{7 π}{4} + 2 πn

Solve

x - \frac{π}{2} = \frac{5 π}{4} + 2 πn : x = 2 πn + \frac{7 π}{4}

Solve

x - \frac{π}{2} = \frac{7 π}{4} + 2 πn : x = 2 πn + \frac{9 π}{4}

x = 2 πn + \frac{7 π}{4}, x = 2 πn + \frac{9 π}{4}

tan (2 t) + tan (t) = 1 - tan (2 t) tan (t)

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

- 2 cos (2 x) = 3

(tan (x) - 1) (2 sin (x) - 3) = 0

tan (θ) (1 + tan^{2} (θ)) = 0

What is the general solution for 2sin(x-pi/2)+sqrt(2)=0 ?
The general solution for 2sin(x-pi/2)+sqrt(2)=0 is x=2pin+(7pi)/4 ,x=2pin+(9pi)/4