Question

Write the expression in the simplest form:
Sec^2A - 1/(cosec^2A -1)

Answer 1

Step-by-step explanation:

$= {sec}^{2} a - \frac{1}{ {cos}^{2} a - 1} \\ = \frac{{ {sec}^{2} a \times { \cos }^{2}a - 1} - 1 }{ {cos}^{2} a - 1} \\ = \frac{ {sec}^{2} a \times {cot}^{2}a - 1 }{ {cot}^{2} a } \\ = {sec}^{2} a - {tan}^{2} a \\ = 1$