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

The general solution for sqrt(2)sin(x)=cos(x) is x=0.61547…+pin

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sqrt(2)sin(x)=cos(x)

2 sin (x) = cos (x)

x = 0.61547 \dots + πn

Degrees

x = 35.26438 \dots^{\circ} + 18 0^{\circ} n

Solution steps

2 sin (x) = cos (x)

Rewrite using trig identities

2 sin (x) = cos (x)

Divide both sides by

cos (x), cos (x) \neq = 0

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

Simplify

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

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

2 tan (x) = 1

2 tan (x) = 1

Divide both sides by

2

2 tan (x) = 1

Divide both sides by

2

\frac{2 tan ( x )}{2} = \frac{1}{2}

Simplify

\frac{2 tan ( x )}{2} = \frac{1}{2}

Simplify

\frac{2 tan ( x )}{2} : tan (x)

\frac{2 tan ( x )}{2}

Cancel the common factor:

2

= tan (x)

Simplify

\frac{1}{2} : \frac{2}{2}

\frac{1}{2}

Multiply by the conjugate

\frac{2}{2}

= \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= \frac{2}{2}

tan (x) = \frac{2}{2}

tan (x) = \frac{2}{2}

tan (x) = \frac{2}{2}

Apply trig inverse properties

tan (x) = \frac{2}{2}

General solutions for

tan (x) = \frac{2}{2}

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{2}{2}) + πn

x = arctan (\frac{2}{2}) + πn

Show solutions in decimal form

x = 0.61547 \dots + πn

8 cos (2 x) = 8 - 8 cos (2 x)

- (2) cos (10 t) = (6) sin (10 t)

cot (x) = \frac{1}{4}

tan (x) = 0, 0 < x < 2 π

x, sin (x) + cos (y) = 2 y

What is the general solution for sqrt(2)sin(x)=cos(x) ?
The general solution for sqrt(2)sin(x)=cos(x) is x=0.61547…+pin