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

The general solution for cos(x+pi/2)-cos(x-pi/2)=sqrt(2) is x=(5pi)/4+2pin,x=(7pi)/4+2pin

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

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

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

Solution steps

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

Rewrite using trig identities

- 2 sin (x) = 2

Divide both sides by

- 2

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

General solutions for

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

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

tan (2 x) + 1 = sec (2 x)

sin (x) \cdot cos (x) = 0

sin (x) - 5 = cos (x) - 5

cot^{2} (x) csc^{2} (x) - cot^{2} (x) = 9

2 sin (θ) + sin (2 θ) = 0

What is the general solution for cos(x+pi/2)-cos(x-pi/2)=sqrt(2) ?
The general solution for cos(x+pi/2)-cos(x-pi/2)=sqrt(2) is x=(5pi)/4+2pin,x=(7pi)/4+2pin