sec^2 x − 1 /sin^2 x

Question

trigonometric expression

Answer 1

(sec^2(x) - 1) / sin^2(x)

sec(x) = 1/cos(x)

( 1/cos^2(x) -1 ) / sin^2(x)

let's multiply the top and bottom by cos^2(x)

( 1 - cos^2(x) ) / (sin^2(x) * cos^2(x))

sin^2(x) / (sin^2(x) * cos^2(x))

1 / cos^2(x)

sec^2(x)