Question

express sinA in terms of cotA

Answer 1

cosec²x - cot²x = 1
cosec²x = 1 + cot²x
1/sin²x = 1 + cot²x
= > sin²x = 1/1+cot²x
Therefore , 
                 sinx = √1/1+cot²x

Answer 2

1/sin²A=cosec²
cosec²A - cot²A = 1
(putting the value of cosec²A)
1/sin²A - cot²A = 1
1/sin²A = 1 + cot²A
sin²A = 1/1 + cot²A
sinA = √1/1 +  cot²A