Question

Question 15: If tan¯¹ x-1 - x-2 + tan¯¹ x+1/x-1 = π/4 then find the value of x.

Class 12 - Math - Inverse Trigonometric Functions

Answer 1

Hey there!!!

⇒ tan¯¹ x-1 - x-2 + tan¯¹ x+1/x-1 = π/4
⇒ tan¯¹ [ { (x+1 / x-2) + (x+1 / x+2) } / { 1- ( x-1 / x-2) (x+1 / x+2) } ] = π/4
⇒ tan¯¹ [  { (x-1)(x+2) + (x+1)(x-2) } / { (x+2)(x-2) - (x-1)(x+1) }  ] = π/4
⇒ tan¯¹ [ (x² + x - 2 + x² - x - 2 ) / ( x² - 4 - x² + 1) ] = π/4
⇒ tan¯¹ [ 2x²-4 / -3] = π/4

Multiplying both sides by tan →

⇒  (4-2x²) / 3 = 1
⇒ 4 - 2x² = 3
⇒ 2x² = 4 - 3
⇒ 2x² = 1
⇒ x = +1/√2 or x = -1/√2

These are the possible values of x.

HOPE IT HELPS!!!

Answer 2

vertically opposite angles are congruent