If cosec x + cot x = α,

Question:

If cosec x + cot x = α, then sin x = _________.

Solution:

Given cosec x + cot x =      ...(1)

Since cosec2– cot2x = 1

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

i.e (cosec x – cot xa = 1

i. $\mathrm{e} \operatorname{cosec} x-\cot x=\frac{1}{a}$   ...92)

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

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