What is the general solution for cos(x)+sin(x)=(sqrt(6))/2 ?

The general solution for cos(x)+sin(x)=(sqrt(6))/2 is x=2pin+pi/(12),x=2pin+(5pi)/(12)

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cos(x)+sin(x)=(sqrt(6))/2

cos (x) + sin (x) = \frac{6}{2}

x = 2 πn + \frac{π}{12}, x = 2 πn + \frac{5 π}{12}

Solution steps

cos (x) + sin (x) = \frac{6}{2}

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = \frac{6}{2}

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{3}{2}

General solutions for

sin (x + \frac{π}{4}) = \frac{3}{2}

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

Solve

x + \frac{π}{4} = \frac{π}{3} + 2 πn : x = 2 πn + \frac{π}{12}

Solve

x + \frac{π}{4} = \frac{2 π}{3} + 2 πn : x = 2 πn + \frac{5 π}{12}

x = 2 πn + \frac{π}{12}, x = 2 πn + \frac{5 π}{12}

6 tan^{2} (x) - 2 = 0

tan (x) = \infty

2 arctanh (\frac{( x - 2 )}{( x + 1 )}) = ln (2)

tan (x) = - 1.5

2 cos^{2} (x) + cos (x) - 3 = 0

What is the general solution for cos(x)+sin(x)=(sqrt(6))/2 ?
The general solution for cos(x)+sin(x)=(sqrt(6))/2 is x=2pin+pi/(12),x=2pin+(5pi)/(12)