Question

Write the value of cot^2titha-1/sin^2titha

Answer 1

(I am taking tita= A for my convenience)
we know that cot²A = cos²A/sin²A
substitute that in the equation
we get,
  cos²A/sin²A - 1/sin²A = -1
now,
cos²A-1/sin²A = -1
⇒ -(1-cos²A)/sin²A = -1
as [1-cos²A = sin²A]
  -(sin²A)/sin²A = -1
 -1=-1
  hence proved
 hope u have understood the answer

Answer 2

${cot}^{2} \alpha - \frac{1}{ {sin}^{2} \alpha } \\ {cot}^{2} \alpha - {cosec}^{2} \\ \frac{ {cos}^{2} \alpha }{ {sin}^{2} \alpha } - \frac{1}{ {sin}^{2} \alpha } \\ \frac{ ({cos}^{2} \alpha - 1) }{ {sin}^{2} \alpha } \\ - \frac{(1 - {cos}^{2} \alpha ) }{ {sin}^{2} \alpha } \\ - \frac{ {sin}^{2} \alpha }{ {sin}^{2} \alpha } \\ = - 1$