Example 5 - Chapter 2 Class 12 Inverse Trigonometric Functions
Last updated at April 16, 2024 by Teachoo
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Ex 2.2, 5 Important
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Ex 2.2, 4 Important
Example 4 Important
Misc 9 Important
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Ex 2.2, 6
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Ex 2.2, 7 Important
Ex 2.2, 3 Important
Ex 2.2, 9 Important
Misc 10 Important
Misc 8 Important
Not clear how to approach
Last updated at April 16, 2024 by Teachoo
Example 5 Write cotโ1 (1/โ(๐ฅ^2 โ 1)), |๐ฅ| > 1 in the simplest form. cot-1 (1/โ(๐ฅ^2 โ 1)) Putting x = sec ฮธ = cotโ1 (1/โ(ใ๐ฌ๐๐ใ^๐โก๐ โ 1)) = cotโ1 (1/โ(ใ(๐ + ใ๐ญ๐๐งใ^๐ใโก๐ฝ ) โ 1)) = cotโ1 (1/โ(tan^2โกฮธ )) We write 1/โ(๐ฅ^2 โ 1) in form of cot Whenever there is โ(๐ฅ^2โ1) , we put x = sec ฮธ = cotโ1 (1/tanโกฮธ ) = cotโ1 (cot ฮธ) = ฮธ We assumed x = sec ฮธ sec ฮธ = x ฮธ = secโ1 x Hence, our equation becomes cotโ1 (1/โ(๐ฅ^2โ1)) = ฮธ cotโ1 (1/โ(๐ฅ^2โ1)) = secโ1 x