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 June 23, 2025 by Teachoo

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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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