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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