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Popular >

solvefor x,arctan(|x-y|)>0

Solution

solve for

x, arctan (∣ x - y ∣) > 0

Solution

No Solution for x \in R

Solution steps

arctan (∣ x - y ∣) > 0

If

arctan (x) > a

then

x > tan (a)

∣ x - y ∣ > tan (0)

tan (0) = 0

tan (0)

Use the following trivial identity:

tan (0) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 0

∣ x - y ∣ > 0

∣ x - y ∣ > 0 :

False for all

x \in R

∣ x - y ∣ > 0

Apply absolute rule: If

∣ u ∣ > 0

then

u < 0

or

u > 0

x - y < 0 or x - y > 0

x - y < 0 or x - y > 0

x - y < 0 or x - y > 0

x - y < 0 : x < y

x - y < 0

Move

y

to the right side

x - y < 0

Add

y

to both sides

x - y + y < 0 + y

Simplify

x < y

x < y

x - y > 0 : x > y

x - y > 0

Move

y

to the right side

x - y > 0

Add

y

to both sides

x - y + y > 0 + y

Simplify

x > y

x > y

Combine the intervals

False for all x \in R or False for all x \in R

False for all x \in R or False for all x \in R

No Solution for x \in R

No Solution for x \in R

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