Question 21
If cot^(-1) (3x+5)>π/4, then find the range of the values of x.
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CBSE Class 12 Sample Paper for 2025 Boards
CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Dec. 13, 2024 by Teachoo
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Transcript
Question 21 If cot^(โ1) (3๐ฅ+5)>๐/4, then find the range of the values of ๐ฅ.Given ใ๐๐๐กใ^(โ1) (3๐ฅ+5)>๐/4 Taking cot^(โ1) on other side, Sign of inequality changes because cot^(โ1) is a decreasing function ๐๐+๐<๐๐๐โกใ๐ /๐ใ Putting ๐๐๐กโกใ๐/4ใ = 1 3๐ฅ+5<1 3๐ฅ<1โ5 3๐ฅ<โ4 Note: Here cot^(โ1) is a decreasing function. This means As x increases cot^(โ1) decreases For example ใ๐๐๐ใ^(โ๐) โ๐<ใ๐๐๐ใ^(โ๐) ๐ as 30ยฐ < 45ยฐ But, if we remove ใ๐๐๐ใ^(โ๐) โ๐>๐ So, when we remove cot^(โ1), we have to change the sign of inequality ๐<(โ๐)/๐ So, ๐ โ(โโ,(โ๐)/๐)