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Ex 2.2, 6 - Simplify: tan-1 1/root (x2-1) - Class 12 Inverse

Ex 2.2, 6 - Chapter 2 Class 12 Inverse Trigonometric Functions - Part 2

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Ex 2.2, 6 Write the function in the simplest form: tanβˆ’1 1/√(π‘₯^2βˆ’1), |x| > 1 tanβˆ’1 (1/√(π‘₯^2 βˆ’ 1)) Putting x = sec ΞΈ = tanβˆ’1 (1/√(〖𝒔𝒆𝒄〗^𝟐⁑𝜽 βˆ’ 1)) = tanβˆ’1 (1/√(γ€–(𝟏 + 〖𝒕𝒂𝒏〗^πŸγ€—β‘πœ½ ) βˆ’ 1)) = tanβˆ’1 (1/√(tan^2⁑θ )) = tanβˆ’1 (1/tan⁑θ ) We write 1/√(π‘₯^2 βˆ’ 1) in form of tan Whenever there is √(π‘₯^2βˆ’1) , we put x = sec ΞΈ = tanβˆ’1 (cot ΞΈ) = tanβˆ’1 tan (90 – ΞΈ) = 90 – ΞΈ = 𝝅/𝟐 – ΞΈ We assumed x = sec ΞΈ sec ΞΈ = x ΞΈ = sec-1 x Hence, our equation becomes tan-1 (1/√(π‘₯^2βˆ’1)) = πœ‹/2 – ΞΈ = 𝝅/𝟐 – secβˆ’1 x (cot ΞΈ = tan (90 – ΞΈ) )

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