`cot^(-1)((alpha)/(2))-tan^(-1)(sqrt(cosalpha))=x`, then sin x is equal to

Options

A. `tan^(2)((alpha)/(2))`
B. `cot^(2)((alpha)/(2))`
C. `tanalpha`
D. `cot((alpha)/(2))`

Answer

A

Explanation

Given, `tan^(-1)((1)/(sqrt(cosalpha)))`
`-tan^(-1)(sqrt(cosalpha))=x`
`impliestan^(-1)(((1)/(sqrt(cosalpha))-sqrt(cosalpha))/(1+(1)/(sqrt(cosalpha))*sqrt(cosalpha)))=x`
`implies(1-cosalpha)/(2sqrt(cosalpha))=tanx`
`implies(2sqrt(cosalpha))/(1-cosalpha)=cotx`
`implies"cosec x"=(1+cosalpha)/(1-cosalpha)`
`implies sinx=(1-cosalpha)/(1+cosalpha)`
`impliesx=(2sin^(2)((alpha)/(2)))/(2cos^(2)((alpha)/(2)))=tan^(2)((alpha)/(2))`