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Question: cot<sup>–1</sup>\(( \sqrt { \cos } \alpha )\) – tan<sup>–1</sup> \(( \sqrt { \cos } \alpha )\) = x t...

cot–1(cos⁡α)( \sqrt { \cos } \alpha ) – tan–1 (cos⁡α)( \sqrt { \cos } \alpha ) = x then sin x =

A

tan2 α2\frac { \alpha } { 2 }

B

cot2 (α2)\left( \frac { \alpha } { 2 } \right)

C

tan a

D

cosα2\frac { \alpha } { 2 }

Answer

tan2 α2\frac { \alpha } { 2 }

Explanation

Solution

cot–1cos⁡α\sqrt { \cos \alpha }– tan–1 cos⁡α\sqrt { \cos \alpha } = x

π2\frac { \pi } { 2 } – 2tan–1 cos⁡α\sqrt { \cos \alpha } = x Ž π2\frac { \pi } { 2 } – tan–1(2cos⁡α1−cos⁡α)\left( \frac { 2 \sqrt { \cos \alpha } } { 1 - \cos \alpha } \right) = x

cotx = 2cos⁡α1−cos⁡α\frac { 2 \sqrt { \cos \alpha } } { 1 - \cos \alpha }Ž cosec x =

= (α2)\left( \frac { \alpha } { 2 } \right)