What is the general solution for sin(x/2)+cos(x/2)=1 ?

The general solution for sin(x/2)+cos(x/2)=1 is x=4pin,x=4pin+pi

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sin(x/2)+cos(x/2)=1

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

x = 4 πn, x = 4 πn + π

Solution steps

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

Rewrite using trig identities

2 sin (\frac{x}{2} + \frac{π}{4}) = 1

Divide both sides by

2

sin (\frac{x}{2} + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (\frac{x}{2} + \frac{π}{4}) = \frac{2}{2}

\frac{x}{2} + \frac{π}{4} = \frac{π}{4} + 2 πn, \frac{x}{2} + \frac{π}{4} = \frac{3 π}{4} + 2 πn

Solve

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

Solve

\frac{x}{2} + \frac{π}{4} = \frac{3 π}{4} + 2 πn : x = 4 πn + π

x = 4 πn, x = 4 πn + π

cos (2 x) = 3 sin (2 x)

3 sin (2 x - 1 5^{\circ}) = cos (2 x - 1 5^{\circ})

sec (\frac{x}{2}) - 2 = 0

sin (x) = \frac{12}{20}

sin (x) = 2 π

What is the general solution for sin(x/2)+cos(x/2)=1 ?
The general solution for sin(x/2)+cos(x/2)=1 is x=4pin,x=4pin+pi