Question

Q.6. Find the value of cot(arctan(z) + arccot(z))​

Answer 1

Let, arctan(x) = e Therefore, x = tan 0 x = cot(pi/2 - theta), [Since, cot(pi/2 - theta) = tan theta]; Rightarrow cot^ -1 x= pi 2 - theta cot 1 2 X= tan x, [Since, theta = arctan(x); Rightarrow cot^ -1 x+tan^ -1 x= pi 2; Rightarrow tan^ -1 x+cot^ -1 x= pi 2 Therefore, tan 1 ^ - 1 + arccot(x) = pi/2