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Write the following functions in the simplest form : tan^(-1)(1/sqrt(x^2 -1)), |x| gt 1

Answer»

SOLUTION :PUT x = sec`theta, theta sec^(-1)x`
Then `TAN^(-1)(1/sqrt(x^2-1)) = tan^(-1)(1/sqrt(sec^2 theta -1)) = tan^(-1)(1/tan theta)`
`= tan^(-1) COT theta = tan^(-1)tan(pi/2- theta) = pi/2-sec^(-1)x`


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