sec^2 x -1 / sin^2x

Answer 1

Because 1 + tan²(x) + = sec²(x) we can say tan²(x) = sec²(x) - 1 so replace the numerator with tan²(x). Then, because tan²(x) = sin²(x)/cos²(x), replace the tan²(x). Now we have sin²(x)/[cos²(x)sin²(x)]. The sin²(x) in the numerator cancels the sin²(x) in the denominator resulting in 1/cos²(x) which is sec²(x)