# trigonometry repost

posted by
**Anonymous**
.

Reduce (csc^2 x - sec^2 X) to an expression containing only tan x.

(is this correct?)

csc x = 1/sin x

sec x = 1/cos x

tan x = 1/cot x

sin^2 x + cos^2 x = 1

1 + cot^2 x = csc^2 x

tan^2 x + 1 = sec^2 x

csc^2 x - sec^2 x

= 1 + cot^2 x - (1 + tan^2 x)

= cot^2 x - tan^2 x

= (1/tan^2 x) - tan^2 x