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.

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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)

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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

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