trigonometry

Question

prove 

 

 

Cos x       cot x

_____ -  ______   = cos ² x  ^_  cot ² x   

sec x       tan x.      

Answer 1

Use the inverse identities!

Answer 2

We know,

Cosx = 1/Secx

Cotx = 1/Tanx

Then, we are given

LHS as

cosx/secx -cotx/tanx

Cosx * 1/Secx - Cotx*1/Tanx

Cosx * Cosx - Cotx * Cotx

Cos²x - Cot²x = RHS

PROVED

Answer 3

Think of it like this:

 

secant = 1/cosine

 

cotangent = 1/tangent

 

so think of it like this:

  cotangent on the top = tangent on the bottom

  cotangent on the bottom = tangent on the top

 

  secant on the top = cosine on the bottom

  secant on the bottom = cosine on the top

 

 

cos/sec  - cot/tan =

 

cos*cos - 1/(tan*tan)  <---- sec = 1/cos so  sec goes to the top and becomes cosine

                                      cot = 1/tan so tangent goes to the bottom

 

= cos^2 - 1/tan^2 <--- properties of exponents:  N*N = N^2

 

= cos^2 - (1/tan)^2 <--- properties of exponents:  (1/N^2) = (1/N)^2

 

= cos^2  - cot^2