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

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

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

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

tan (\frac{x}{2}) = 1

General solutions for

tan (\frac{x}{2}) = 1

\frac{x}{2} = \frac{π}{4} + πn

Solve

\frac{x}{2} = \frac{π}{4} + πn : x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

tan^{2} (x) = 1 - sec (x)

tan (x) sin (x) + 2 sin (x) = 0

cos (4 x) - cos (2 x) = 0

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

2 cos (θ) = - 2

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