Answer
True.
Work Step by Step
Verify the following identity:
$\frac{sin(x) - 1}{sin(x) + 1}= \frac{-cos(x)^2}{(sin(x) + 1)^2}$
Cross multiply:
$(sin(x) - 1) (1 + sin(x)) = ^?-cos^2(x)$
Since $(sin(x) - 1) (1 + sin(x)) = sin(x)^2 - 1$:
$sin(x)^2 - 1 = ^?-cos^2(x)$
Since $sin^2(x) = 1 - cos^2(x)$:
$1 - cos^2(x) - 1 = ^?-cos^2(x)$
Since $-1 + 1 - cos^2(x) = -cos^2(x)$:
$-cos^2(x) = ^?-cos^2(x)$
The left hand side and right hand side are identical, thus verifying the identity.
