Question

If u = cot^–1 $\sqrt { \tan \alpha }$ – tan^–1 $\sqrt { \tan \alpha }$ , then tan $\left( \frac { \pi } { 4 } - \frac { \mu } { 2 } \right)$is equal

to–

• A. $\sqrt { \tan \alpha }$
• B. $\sqrt { \cot \alpha }$
• C. tan a
• D. cot a

Answer 1

Answer: (A)

$\sqrt { \tan \alpha }$

Answer 2

Let $\sqrt { \tan \alpha }$ = tan x, then u = cot^–1(tan x) – tan^–1

(tan x) = $\frac { \pi } { 2 }$ – x – x = $\frac { \pi } { 2 }$ – 2x

Ž 2x = $\frac { \pi } { 2 }$ – u Ž x = $\frac { \pi } { 4 }$ – Ž tan x = tan

Ž $\sqrt { \tan \alpha }$= tan .