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

The general solution for sin(x)+cos(x)= 1/(sqrt(2)) is x=2pin-pi/(12),x=2pin+(7pi)/(12)

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

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

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

Solution steps

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

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = \frac{1}{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}

cot (x) = 4

sin (x) = 0.2765

tan^{2} (x) = - \frac{3}{2} sec (x)

7 cos (θ) = 3 + cos (θ)

2 sin^{2} (x) - 9 sin (x) + 4 = 0

What is the general solution for sin(x)+cos(x)= 1/(sqrt(2)) ?
The general solution for sin(x)+cos(x)= 1/(sqrt(2)) is x=2pin-pi/(12),x=2pin+(7pi)/(12)