Identities

Question

verify the identity

sec^2x cot x - cot x =tan x

Answer 1

multiply both sides by 1/cotx.  On the left by the form 1/cotx  and on the right by tanx since 1/cotx = tanx

 

sec²x - 1 = tan²x  

which is a recognized identity.

 

∴ confirmed

Answer 2

sec^2xcotx-cotx=tanx

cotx(sec^2x-1)=tanx

1+tan^2x=sec^2x

tan^2x=sec^2x-1

substitute

cotx(tan^2x)=tanx

cotx=1/tanx

substitute

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

tanx=tanx

Answer 3

 

Hi Cierra,

 

sec²(x)cot(x) - cot(x)

 

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

 

         ( as sec(x) = 1/cos(x), cot(x) = cos(x)/sin(x) )

 

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

 

       = 1/[sin(x)cos(x)] - cos²(x)/[sin(x)cos(x)]

 

       = [1 - cos²(x)]/[sin(x)cos(x)]

 

       = sin²(x)/[sin(x)cos(x)]

 

         ( as sin²(x) = 1 - cos²(x) )

 

       = sin(x)/cos(x)

 

       = tan(x)               [Q.E.D.]

 

Hope this helps.