What is the general solution for sin(x)+cos(x)=sqrt(3/2) ?

The general solution for sin(x)+cos(x)=sqrt(3/2) is x=2pin+pi/(12),x=2pin+(5pi)/(12)

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sin(x)+cos(x)=sqrt(3/2)

sin (x) + cos (x) = \frac{3}{2}

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

Solution steps

sin (x) + cos (x) = \frac{3}{2}

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = \frac{3}{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}

cos (2 x) - sin (x) = 0.5

cos (θ) - 2 sin^{2} (θ) = - 1

4 + 4 cos (θ) = 0

- cot (2 θ) = 0

1 - \frac{1}{2} \cdot cos (3 θ) = \frac{4 - 2}{4}, 0^{\circ} \leq θ \leq 36 0^{\circ}

What is the general solution for sin(x)+cos(x)=sqrt(3/2) ?
The general solution for sin(x)+cos(x)=sqrt(3/2) is x=2pin+pi/(12),x=2pin+(5pi)/(12)