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

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

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

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

x = 4 πn + \frac{π}{2}

Solution steps

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

Rewrite using trig identities

2 sin (\frac{x}{2} + \frac{π}{4}) = 2

Divide both sides by

2

sin (\frac{x}{2} + \frac{π}{4}) = 1

General solutions for

sin (\frac{x}{2} + \frac{π}{4}) = 1

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

Solve

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

x = 4 πn + \frac{π}{2}

cos (θ) = - \frac{1}{2}, 0 \leq θ < 2 π

2 tan (x) - 16 = 0, 0 \leq x < \frac{π}{2}

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

4 sec (x) + 6 = - 2

tan (2 x) = \frac{1}{4}

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