Precalc: Identities

Question

Prove the following:

sinx(tan^2x+1)=tanxsecx

Answer 1

You know that        tan²x + 1 = sec²x

 

 

Then,

 

sinx(tan²x + 1) =

 

sinx(sec²x) =

 

sinx / (cos²x) =

 

(sinx / cosx) * (1 / cosx) =

 

tanxsecx