Example 13 - Solve tan-1 2x + tan-1 3x = pi/4 - Class 12 - Formulae based

  1. Chapter 2 Class 12 Inverse Trigonometric Functions
  2. Serial order wise
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Example 13 Solve tan–1 2x + tan–1 3x = π/4 We know that tan–1 x + tan–1 y = tan–1 ((𝐱 + 𝐲)/(𝟏 − 𝐱𝐲)) tan-1 2x + tan 3x = tan–1 ((2x + 3x)/(1 − 2x × 3x)) = tan–1 (5x/(1 − 6x2)) Now, given tan–1 2x + tan–1 3x = π/4 tan–1 (5x/(1 − 6x2)) = π/4 5x/(1 − 6x2) = tan π/4 5x/(1− 6x2) = 1 5x = 1 × (1 – 6x2) 5x = 1 – 6x2 6x2 + 5x – 1 = 0 6x2 + 6x – x – 1 = 0 6x(x + 1 ) – 1 (x – 1) = 0 (6x – 1) (x + 1) = 0 ∴ 6x – 1 = 0 or x + 1 = 0 x = 1/6 or x = −1

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