Question

Differentiate cot inverse (1-√x)/(1+√x)

Answer 1

Answer:

pi/4 - tan^-1 (x)

Step-by-step explanation:

cot^-1[(1+x)/(1-x)].

=tan^-1[(1-x)/(1+x)].

put x= tanA

=tan^-1 (1-tanA)/(1+tanA).

=tan^-1 [(tan pi/4 - tan A)/(1+tan pi/4.tan A)].

= tan^-1 tan (pi/4-A)).

= pi/4 -A. , putting A=tan^-1(x).

= pi/4 - tan^-1 (x)            

Ans :- pi/4 - tan^-1 (x)