use the fundamental identities to simplify the expression 1c

use the fundamental identities to simplify the expression. 1-cos^2X/sec^2X-1

Solution

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

using trigonomteric identities

tan^2 x = sec^2 x - 1

sin ^2 x + cos ^2 x = 1

sin ^2 x = 1 - cos^2 x

plugging the values in the expression we get

sin^2x / tan^2 x

now tan x = sin x / cos x

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

on simplifying we get

cos^2x