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It is given that A=(tan^(-1)x)^(3)+(cot^...

It is given that `A=(tan^(-1)x)^(3)+(cot^(-1)x)^(3)` where `x gt 0` and `B=(cos^(-1)t)^(2)+(sin^(-1)t)^(2)` where `t in [0, (1)/(sqrt(2))]`, and `sin^(-1)x+cos^(-1)x=(pi)/(2)` for `-1 le x le 1` and `tan^(-1)x +cot^(-1)x=(pi)/(2)` for `x in R`.
The maximum value of B is :

A

`(pi)/(8)`

B

`-(pi)/(8)`

C

`(7pi)/(8)`

D

`-(7pi)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
A
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