What is this trigonometric identity?

[dcowboys107]

Rewrite f(x) = 4csc^2(x) + 9tan^2(x) in terms of cos(x).

NOTE: Expressions such as cos^2(x) must be entered as cos(x)^2 or (cos(x))2.

 

I rewrote csc(x)^2 as 1/1-cos(x)^2 and tan^2 as ((1-cos(x)/cos(x))^2

 

I'm having a hard time simplifying that down to just cos(x).

[Mage]

Hello dcowboys107

I rewrote csc(x)^2 as 1/1-cos(x)^2 and tan^2 as ((1-cos(x)/cos(x))^2

About your tan identity... are you sure? Please post your derivation

[9e0r9e]

sin^2(x) + cos^2(x) = 1

 

dividing through by cos^2(x) gives,

 

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

 

and substitute in