What is the general solution for -120=-90-arctan(0.1)+arctan(0.1x) ?

The general solution for -120=-90-arctan(0.1)+arctan(0.1x) is No Solution for x\in\mathbb{R}

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-120=-90-arctan(0.1)+arctan(0.1x)

- 120 = - 90 - arctan (0.1) + arctan (0.1 x)

No Solution for x \in R

Solution steps

- 120 = - 90 - arctan (0.1) + arctan (0.1 x)

Switch sides

- 90 - arctan (0.1) + arctan (0.1 x) = - 120

arctan (0.1) = arctan (\frac{1}{10})

arctan (0.1)

- 90 - arctan (\frac{1}{10}) + arctan (0.1 x) = - 120

Move

90

to the right side

- 90 - arctan (\frac{1}{10}) + arctan (0.1 x) = - 120

Add

90

to both sides

- 90 - arctan (\frac{1}{10}) + arctan (0.1 x) + 90 = - 120 + 90

Simplify

- arctan (\frac{1}{10}) + arctan (0.1 x) = - 30

- arctan (\frac{1}{10}) + arctan (0.1 x) = - 30

Move

arctan (\frac{1}{10})

to the right side

- arctan (\frac{1}{10}) + arctan (0.1 x) = - 30

Add

arctan (\frac{1}{10})

to both sides

- arctan (\frac{1}{10}) + arctan (0.1 x) + arctan (\frac{1}{10}) = - 30 + arctan (\frac{1}{10})

Simplify

arctan (0.1 x) = - 30 + arctan (\frac{1}{10})

arctan (0.1 x) = - 30 + arctan (\frac{1}{10})

- \frac{π}{2} < arctan (x) < \frac{π}{2}

No Solution for x \in R

What is the general solution for -120=-90-arctan(0.1)+arctan(0.1x) ?
The general solution for -120=-90-arctan(0.1)+arctan(0.1x) is No Solution for x\in\mathbb{R}