Hi Khusboo,

I believe you've missed the squares in your question. The correct question would have been ==> 9cosec²A - 9cot²A is equal to? [If you want a numeric answer]

Solution:

9cosec²A - 9cot²A

= 9(cosec²A - cot²A)

= 9 × 1 [Since cosec²A - cot²A = 1]

= 9

Now if you feel your question was correct i.e. there is no squares involved,

then there would be no numeric solution. However, you can still proceed with the problem as follows:

9CosecA - 9 Cot A

= 9(Cosec A - Cot A )

=9(1 / Sin A - Cos A / Sin A)

= 9(1 - Cos A / Sin A)

= 9(2Sin²(A/2) / 2Sin(A/2)Cos(A/2)) [ Since 1 - Cos A = 2Sin²(A/2) & Sin A = 2Sin(A/2)Cos(A/2)]

= 9(Sin(A/2) / Cos(A/2))

= 9Tan(A/2)

Hope this helps.