Verify the identity: (sec/cos) - (tan/cot) = 1?

Question

i have no idea how to get the left side to equal the right

Answer 1

EZ PZ, let's do each term of the left side separately:

secx / cosx
= secx / 1/secx
= sec²x

tanx/cotx
= tanx / 1/tanx
= tan²x

so it's really sec²x - tan²x, which according to one of the Pythagorean identities is equal to 1. If you do not know that identity, then you would multiply sec²x - tan²x by (cos²x / cos²x) (essentially 1) to get

(1 - sin²x) / cos²x = cos²x / cos²x = 1

Answer 2

Prove the identity.

secθ/cosθ - tanθ/cotθ = 1

Let's start with the left hand side.

Left Hand Side = secθ/cosθ - tanθ/cotθ

= (1/cosθ)/cosθ - (sinθ/cosθ)/(cosθ/sinθ)

= 1/cos²θ - sin²θ/cos²θ = (1 - sin²θ)/cos²θ

= cos²θ/cos²θ = 1 = Right Hand Side

Answer 3

(sec x)/(cos x) - (tan x)/(cot x)

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

Answer 4

hey Chris do u go to school or are u still in school