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

The general solution for sin(x)+cos(x)=(sqrt(2))/2 is x=2pin-pi/(12),x=2pin+(7pi)/(12)

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

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

x = 2 πn - \frac{π}{12}, x = 2 πn + \frac{7 π}{12}

Solution steps

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

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = \frac{2}{2}

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{1}{2}

General solutions for

sin (x + \frac{π}{4}) = \frac{1}{2}

x + \frac{π}{4} = \frac{π}{6} + 2 πn, x + \frac{π}{4} = \frac{5 π}{6} + 2 πn

Solve

x + \frac{π}{4} = \frac{π}{6} + 2 πn : x = 2 πn - \frac{π}{12}

Solve

x + \frac{π}{4} = \frac{5 π}{6} + 2 πn : x = 2 πn + \frac{7 π}{12}

x = 2 πn - \frac{π}{12}, x = 2 πn + \frac{7 π}{12}

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

t, A (- sin (wt + d) w) = 0

sin (\frac{3 x}{2} + 4 5^{\circ}) = 0

4 sin (2 θ) - 5 sin (θ) = 0

sin^{2} (x) - cos^{2} (x) = sin (x)

What is the general solution for sin(x)+cos(x)=(sqrt(2))/2 ?
The general solution for sin(x)+cos(x)=(sqrt(2))/2 is x=2pin-pi/(12),x=2pin+(7pi)/(12)