Question 21 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at August 14, 2026 by Teachoo

Question 21

If cot^(-1) (3x+5)>π/4, then find the range of the values of x.

-lock-

Question 21 - If cot-1 (3x + 5) >𝜋/4, then find range of values of x - CBSE Class 12 Sample Paper for 2025 Boards

part 2 - Question 21 - CBSE Class 12 Sample Paper for 2025 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

-endlock-

Next: Question 22 → Remove Ads

Teachoo · Class 12 Explore Class 12

Transcript

Question 21 If cot^(−1) (3𝑥+5)>𝜋/4, then find the range of the values of 𝑥.Given 〖𝑐𝑜𝑡〗^(−1) (3𝑥+5)>𝜋/4 Taking cot^(−1) on other side, Sign of inequality changes because cot^(−1) is a decreasing function 𝟑𝒙+𝟓<𝒄𝒐𝒕⁡〖𝝅/𝟒〗 Putting 𝑐𝑜𝑡⁡〖𝜋/4〗 = 1 3𝑥+5<1 3𝑥<1−5 3𝑥<−4 Note: Here cot^(−1) is a decreasing function. This means As x increases cot^(−1) decreases For example 〖𝒄𝒐𝒕〗^(−𝟏) √𝟑<〖𝒄𝒐𝒕〗^(−𝟏) 𝟏 as 30° < 45° But, if we remove 〖𝒄𝒐𝒕〗^(−𝟏) √𝟑>𝟏 So, when we remove cot^(−1), we have to change the sign of inequality 𝒙<(−𝟒)/𝟑 So, 𝒙 ∈(−∞,(−𝟒)/𝟑)

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.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular