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Popular >

1-tan(x)<2

Solution

1 - tan (x) < 2

Solution

- \frac{π}{4} + πn < x < \frac{π}{2} + πn

+2

Interval Notation

(- \frac{π}{4} + πn, \frac{π}{2} + πn)

Decimal Notation

- 0.78539 \dots + πn < x < 1.57079 \dots + πn

Solution steps

1 - tan (x) < 2

Move

1

to the right side

1 - tan (x) < 2

Subtract

1

from both sides

1 - tan (x) - 1 < 2 - 1

Simplify

- tan (x) < 1

- tan (x) < 1

Multiply both sides by

- 1

- tan (x) < 1

Multiply both sides by -1 (reverse the inequality)

(- tan (x)) (- 1) > 1 \cdot (- 1)

Simplify

tan (x) > - 1

tan (x) > - 1

If

tan (x) > a

then

arctan (a) + πn < x < \frac{π}{2} + πn

arctan (- 1) + πn < x < \frac{π}{2} + πn

Simplify

arctan (- 1) : - \frac{π}{4}

arctan (- 1)

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 1) = - arctan (1)

= - arctan (1)

Use the following trivial identity:

arctan (1) = \frac{π}{4}

arctan (1)

x 0 \frac{3}{3} 13 arctan (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} arctan (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ}

= \frac{π}{4}

= - \frac{π}{4}

- \frac{π}{4} + πn < x < \frac{π}{2} + πn

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