If cosec x + cot x = α,

Given cosec x + cot x = a      ...(1)

Since cosec2x – cot2x = 1

(cosec x – cot x) (cosec x + cot x) = 1

i.e (cosec x – cot x) a = 1

i. $\mathrm{e} \operatorname{cosec} x-\cot x=\frac{1}{a}$   ..(2)

adding (1) and (2)

$2 \operatorname{cosec} x=a+\frac{1}{a}$

$2 \operatorname{cosec} x=\frac{a^{2}+1}{a}$

$\frac{2 a}{a^{2}+1}=\frac{1}{\operatorname{cosec} x}$

i. e $\sin x=\frac{2 a}{a^{2}+1}$