Question 7 - Formulae based - Chapter 2 Class 12 Inverse Trigonometric Functions

Last updated at July 15, 2026 by

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

Example 13 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2
Example 13 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 3

Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 5 questions, selected from your answers, mistakes, and progress.
Remove Ads

Transcript

Question 7 Solve tan–1 2x + tan–1 3x = π/4 Given tan–1 2x + tan 3x = π/4 tan–1 ((2x + 3x)/(1 − 2x × 3x)) = π/4 𝟓𝐱/(𝟏 − 𝟔𝐱𝟐) = tan 𝝅/𝟒 We know that tan–1 x + tan–1 y = tan–1 ((𝐱 + 𝐲)/(𝟏 − 𝐱𝐲)) Replacing x by 2x & y by 3x 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 Thus, x = 1/6 or x = −1 But For x = −1 tan–1 2x + tan–1 3x = π/4 tan–1 (–2) + tan–1 (–3) = π/4 So, L.H.S becomes negative but R.H.S is positive. Thus, x = –1 is not possible. Hence, x = 𝟏/𝟔 is the only solution of the given equation

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.