निम्नलिखित फलनों को सरलतम

1.	निम्नलिखित फलनों को सरलतम रूप में लिखिए।V1+-1-1* 03,tan-/ VIf-r
Answer» Let x = tan AA = tan^-1 x tan^-1[{sqrt(1+x^2) - 1}/x] = tan^-1[{sqrt(1 + tan^2 A) - 1}/tan A] = tan^-1[{sqrt(sec^2 A) - 1}/tan A] = tan^-1[{sec A - 1}/tan A] = tan^-1[(1/cos A - 1)/sin A/cos A] = tan^-1[(1 - cos A)/sin A] = tan^-1[(2 sin^2 A/2)/(2sinA/2.cosA/2)] = tan^-1[ tan A/2] = A/2 = 1/2 tan^-1 x

निम्नलिखित फलनों को सरलतम रूप में लिखिए।V1+-1-1* 03,tan-/ VIf-r

Answer»

Let x = tan AA = tan^-1 x

tan^-1[{sqrt(1+x^2) - 1}/x]

= tan^-1[{sqrt(1 + tan^2 A) - 1}/tan A]

= tan^-1[{sqrt(sec^2 A) - 1}/tan A]

= tan^-1[{sec A - 1}/tan A]

= tan^-1[(1/cos A - 1)/sin A/cos A]

= tan^-1[(1 - cos A)/sin A]

= tan^-1[(2 sin^2 A/2)/(2sinA/2.cosA/2)]

= tan^-1[ tan A/2]

= A/2

= 1/2 tan^-1 x