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

The general solution for cos(x)=sin(x-pi/2) is x= pi/2+2pin,x=(3pi)/2+2pin

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

cos (x) = sin (x - \frac{π}{2})

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

cos (x) = sin (x - \frac{π}{2})

Rewrite using trig identities

cos (x) = - cos (x)

Subtract

- cos (x)

from both sides

2 cos (x) = 0

Divide both sides by

2

cos (x) = 0

General solutions for

cos (x) = 0

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

5 cos (x) + 2 = 0, 0 \leq x \leq 2 π

2 sin (x) cos (x) - sin (2 x) cos (2 x) = 0

cos (x) = \frac{21}{29}

\frac{4}{sin ( 104.4 8 ^{\circ} )} = \frac{2}{sin ( a )}

sin (x + \frac{3 π}{2}) - cos (x + \frac{π}{2}) = 1

What is the general solution for cos(x)=sin(x-pi/2) ?
The general solution for cos(x)=sin(x-pi/2) is x= pi/2+2pin,x=(3pi)/2+2pin