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

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

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sin(x)=cos(x+pi/2)

sin (x) = cos (x + \frac{π}{2})

x = 2 πn, x = π + 2 πn

Solution steps

sin (x) = cos (x + \frac{π}{2})

Rewrite using trig identities

sin (x) = - sin (x)

Subtract

- sin (x)

from both sides

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 (θ) = \frac{2}{3}, - \frac{5 π}{2}, 2 π

6 cos (2 x) = 32

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

10 cos (x) + 4 = 10

x, arctan (x) = \frac{π}{4}

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