What is the general solution for tan(x)+1= 1/5 ?

The general solution for tan(x)+1= 1/5 is x=-0.67474…+pin

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tan(x)+1= 1/5

tan (x) + 1 = \frac{1}{5}

x = - 0.67474 \dots + πn

Degrees

x = - 38.65980 \dots^{\circ} + 18 0^{\circ} n

Solution steps

tan (x) + 1 = \frac{1}{5}

Move

1

to the right side

tan (x) + 1 = \frac{1}{5}

Subtract

1

from both sides

tan (x) + 1 - 1 = \frac{1}{5} - 1

Simplify

tan (x) + 1 - 1 = \frac{1}{5} - 1

Simplify

tan (x) + 1 - 1 : tan (x)

tan (x) + 1 - 1

Add similar elements:

1 - 1 = 0

= tan (x)

Simplify

\frac{1}{5} - 1 : - \frac{4}{5}

\frac{1}{5} - 1

Convert element to fraction:

1 = \frac{1 \cdot 5}{5}

= - \frac{1 \cdot 5}{5} + \frac{1}{5}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 1 \cdot 5 + 1}{5}

- 1 \cdot 5 + 1 = - 4

- 1 \cdot 5 + 1

Multiply the numbers:

1 \cdot 5 = 5

= - 5 + 1

Add/Subtract the numbers:

- 5 + 1 = - 4

= - 4

= \frac{- 4}{5}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4}{5}

tan (x) = - \frac{4}{5}

tan (x) = - \frac{4}{5}

tan (x) = - \frac{4}{5}

Apply trig inverse properties

tan (x) = - \frac{4}{5}

General solutions for

tan (x) = - \frac{4}{5}

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

x = arctan (- \frac{4}{5}) + πn

x = arctan (- \frac{4}{5}) + πn

Show solutions in decimal form

x = - 0.67474 \dots + πn

cos (2 x) = \frac{119}{169}

x, 2 cos (x) - 1 = 0

2 sin (2 x) = - 2

tan^{4} (x) + 2 tan^{2} (x) - 7 = 0

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

What is the general solution for tan(x)+1= 1/5 ?
The general solution for tan(x)+1= 1/5 is x=-0.67474…+pin