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

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

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

sin (x + \frac{π}{2}) - sin (x - \frac{π}{2}) = 2

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

Solution steps

sin (x + \frac{π}{2}) - sin (x - \frac{π}{2}) = 2

Rewrite using trig identities

2 cos (x) = 2

Divide both sides by

2

cos (x) = \frac{2}{2}

General solutions for

cos (x) = \frac{2}{2}

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

x, tan (x) csc (x) = \frac{1}{f}

sin (x) = \frac{10.7}{71.5}

cos (y) = 1

sec (x) = - 3

1.5 = \frac{sin ( 4 5 ^{\circ} )}{sin ( x )}

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