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 Dec. 13, 2024 by Teachoo

Question 21

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

-lock-

-endlock-

Next: Question 22 →

You saved atleast 2 minutes by viewing the ad-free version of this page. Thank you for being a part of Teachoo Black.

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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular