Question

cot^2A-1/sin^2A is equal to?.....options are Tan^2A,cot^2A,1,-1

Answer 1

Solution: Equation we have is cot²A - 1/sin²A.

• 1 - cos²A = sin²A
• cot²A = cos²A/sin²A

→ cos²A/sin²A - 1/sin²A

→ (cos²A - 1)/sin²A

→ - (1 - cos²A)/sin²A

→ - sin²A/sin²A

→ - 1

Hence answer is - 1

Answer 2

Answer:

$\large\boxed{\sf{-1}}$

Step-by-step explanation:

${ \cot}^{2} A - \frac{1}{ { \sin }^{2} A} \\ \\ = { \cot }^{2} A - { \csc}^{2} A \\ \\ = { \cot }^{2} A - (1 + { \cot}^{2} A) \\ \\ = { \cot}^{2} A - 1 - { \cot }^{2} A\\ \\ = - 1$

Hence, -1 is the required value.

Concept Map :-

• $\sin( \alpha ) = \dfrac{1}{ \csc( \alpha ) }$

• ${ \csc }^{2} \alpha = 1 + { \cot }^{2} \alpha$