Ex 2.2, 6
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Ex 2.2, 6 Write the function in the simplest form: tan-1 1/√(𝑥^2−1), |x| > 1 tan-1 (1/√(𝑥^2 − 1)) Putting x = sec θ = tan-1 (1/√(sec^2θ − 1)) = tan-1 (1/√(〖(1 + tan^2〗θ ) − 1)) = tan-1 (1/√(〖1 −1 + tan^2〗θ )) = tan-1 (1/√(tan^2θ )) = tan-1 (1/tanθ ) = tan-1 (cot θ) = tan-1 tan (90 – θ) = 90 – θ = 𝜋/2 – θ We assumed x = sec θ sec θ = x θ = sec-1 x Hence tan-1 (1/√(𝑥^2−1)) = 𝜋/2 – θ = 𝜋/2 – sec-1 x
Chapter 2 Class 12 Inverse Trigonometric Functions
Serial order wise
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why we didn't take x = cosecø instead of secø?if we take x = cosec then we get tan~1(1/cotø).