What is the general solution for sin(x/2)-cos(x/2)=0 ?

The general solution for sin(x/2)-cos(x/2)=0 is x= pi/2+2pin

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

sin (\frac{x}{2}) - cos (\frac{x}{2}) = 0

x = \frac{π}{2} + 2 πn

Solution steps

sin (\frac{x}{2}) - cos (\frac{x}{2}) = 0

Rewrite using trig identities

tan (\frac{x}{2}) - 1 = 0

Move

1

to the right side

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

2 sin^{2} (\frac{x}{3}) = 1, - π \leq, x \leq π

cos^{2} (x) + sin^{2} (x) = sin (x) + \frac{1}{2}

sin (A) = 0.53

tan (a) = 3, cos (a)

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

What is the general solution for sin(x/2)-cos(x/2)=0 ?
The general solution for sin(x/2)-cos(x/2)=0 is x= pi/2+2pin