Question

Statement 1: If 0 < x < then the value of tan⁻¹ (cot x) = `x/2 − x`

Statement 2: tan⁻¹(tan x) = x, ∀ x ∈ R

Options

• Statement 1 is true and Statement 2 is false.

• Statement 2 is true and Statement 1 is false.

• Both the staterments are true.

• Both the statements are false.

Answer 1

Statement 1 is true and Statement 2 is false.

Explanation:

Statement 1 is True: Since cot x = tan`(π/2 − x)`, tand in the given range `(0, π/2)` the inverse tangent correctly returns `(π/2 − x)`

Statement 2 is false because the property tan ⁻¹(tan x) = x only holds true when x is within its principal range `(−π/2, π/2)` not for all real numbers.