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

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

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

sin (x) + cos (x) = 1

x = 2 πn, x = 2 πn + \frac{π}{2}

Solution steps

sin (x) + cos (x) = 1

Rewrite using trig identities

2 sin (x + \frac{π}{4}) = 1

Apply rule

1 = 1

2 sin (x + \frac{π}{4}) = 1

Divide both sides by

2

sin (x + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (x + \frac{π}{4}) = \frac{2}{2}

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

Solve

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

Solve

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

x = 2 πn, x = 2 πn + \frac{π}{2}

2 sin^{2} (x) - sin (x) - 1 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

x, z = sin (x^{2} y)

2 tan (x) - 3 = 3 tan (x) - 4

1 + cot (θ) = csc (θ)

tan (x) = cot (2 5^{\circ})

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