What is the general solution for sin(x+pi/6)+cos(x+pi/6)=1 ?

The general solution for sin(x+pi/6)+cos(x+pi/6)=1 is x=2pin-pi/6 ,x=2pin+pi/3

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sin(x+pi/6)+cos(x+pi/6)=1

sin (x + \frac{π}{6}) + cos (x + \frac{π}{6}) = 1

x = 2 πn - \frac{π}{6}, x = 2 πn + \frac{π}{3}

Solution steps

sin (x + \frac{π}{6}) + cos (x + \frac{π}{6}) = 1

Rewrite using trig identities

2 sin (\frac{π}{6} + x + \frac{π}{4}) = 1

Divide both sides by

2

sin (\frac{π}{6} + x + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (\frac{π}{6} + x + \frac{π}{4}) = \frac{2}{2}

\frac{π}{6} + x + \frac{π}{4} = \frac{π}{4} + 2 πn, \frac{π}{6} + x + \frac{π}{4} = \frac{3 π}{4} + 2 πn

Solve

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

Solve

\frac{π}{6} + x + \frac{π}{4} = \frac{3 π}{4} + 2 πn : x = 2 πn + \frac{π}{3}

x = 2 πn - \frac{π}{6}, x = 2 πn + \frac{π}{3}

sin (x) = - 1, 0 \leq x \leq 2 π

- 3 sin (x) + cos (x) = 0

2 sin^{2} (x) + 5 cos (x) - 4 = 0

cos (2 x) = 3 sin (x) - 1

2 sin (2 x) = - 1

What is the general solution for sin(x+pi/6)+cos(x+pi/6)=1 ?
The general solution for sin(x+pi/6)+cos(x+pi/6)=1 is x=2pin-pi/6 ,x=2pin+pi/3