Ex 2.2, 5 - Chapter 2 Class 12 Inverse Trigonometric Functions

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Ex 2.2, 5 Write the function in the simplest form: tan-1 ( (1 + x^2 ) 1)/x , x 0 tan-1 ( (1 + x^2 ) 1)/x Putting x = tan = tan-1 (( (1 + tan^2 ) 1)/(tan )) = tan-1 (( (sec^2 ) 1)/(tan )) = tan-1 ((sec 1)/(tan )) = tan-1 ((1/cos 1)/(sin /cos )) = tan-1 (((1 cos )/cos )/(sin /cos )) = tan-1 ((1 cos )/cos cos /sin ) = tan-1 ((1 cos )/sin ) = tan-1 ((2 2 /2)/(2 sin /2 cos /2 )) = tan-1 ( sin /2 /cos /2 ) = tan-1 ( /2) = /2 We assumed that x = tan = tan-1x Hence, tan-1 ( (1 + x^2 ) 1)/x = /2 = 1/2 tan-1x