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

The general solution for sin(x)=sin(x-pi/2) is x=(3pi)/4+pin

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

sin (x) = sin (x - \frac{π}{2})

x = \frac{3 π}{4} + πn

Solution steps

sin (x) = sin (x - \frac{π}{2})

Rewrite using trig identities

sin (x) = - cos (x)

Subtract

- cos (x)

from both sides

sin (x) + cos (x) = 0

Rewrite using trig identities

tan (x) + 1 = 0

Move

1

to the right side

tan (x) = - 1

General solutions for

tan (x) = - 1

x = \frac{3 π}{4} + πn

tan (x) = \frac{π}{3}

- 7 tan (a) - 14 = tan (a) - 6

cos (x) = - 0.58

tan^{4} (x) - 4 tan^{2} (x) + 3 = 0

sin (2 x) = \frac{21}{25}

What is the general solution for sin(x)=sin(x-pi/2) ?
The general solution for sin(x)=sin(x-pi/2) is x=(3pi)/4+pin