Please explain number 14 15 and 18 3 COS x 0 7 12 cotx sin

Please explain number 14, 15 and 18

= 3, COS x 0 7 12, cotx=, sin x

14) cot^2 x - csc^2 x

cot x = cos x / sin x

csc x = 1/ sin x

so we can write

cot^2 x - csc^2 x = cos^2 x / sin^2 x - 1/ sin^2 x

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

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

= -1

b is mathched with 14

15_ cos x ( 1+ tan^2 x )

( 1 + tan^2 x ) = sec^2 x

cos x ( sec^2 x )

sec x = 1/ cos x

cos x ( 1/ cos^2 x )

= 1 / cos x

= sec x

hence, 15 is matched with f

18) cos ^2 [ (pi/2) - x ] / cos x

cos ( pi/2 -x ) = sin x

cos ^2 [ (pi/2) - x ] = sin^2 x

sin^2 x / cos x

= tan x sin x

18 is matched with d