What is the general solution for tan(x)= 1/(sqrt(2)) ?

The general solution for tan(x)= 1/(sqrt(2)) is x=0.61547…+pin

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tan(x)= 1/(sqrt(2))

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

x = 0.61547 \dots + πn

Solution steps

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

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}

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

7 cos (x) + 3 = 3 cos (x) + 2

2 sin (2 θ) + 1 = 0

sin (2 x) - 2 sin (x) = 0

7 cos^{2} (x) - 1 = 5 cos (x)

x, sin (2 x) = 0

What is the general solution for tan(x)= 1/(sqrt(2)) ?
The general solution for tan(x)= 1/(sqrt(2)) is x=0.61547…+pin