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

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

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

sin (x - \frac{π}{2}) = cos (x)

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

Solution steps

sin (x - \frac{π}{2}) = cos (x)

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

cos (θ) = \frac{6}{14 \cdot 9}

sin (θ + \frac{π}{4}) = \frac{1}{2}

(cot (x) - 1) (sin (x) - 1) = 0

x, sin (y) + cos (x) = 1

x, u = cos (x)

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