How do you verify the identity (tan^3alpha-1)/(tanalpha-1)=tan^2alpha+tanalpha+1?

1 Answer
Apr 19, 2017

see below

Explanation:

Use the Factors for Difference of Two Cubes

color(red)(x^3 -y^3=(x-y)(x^2+xy+y^2)

Left hand Side:

color(red)((tan^3 alpha-1)/(tan alpha-1)=color(blue)(((tan alpha-1)(tan^2 alpha+tan alpha *1+1))/(tan alpha-1)

color(blue)(=(cancel((tan alpha-1))(tan^2 alpha+tan alpha+1))/cancel(tan alpha-1)

color(blue)(=tan^2 alpha+tan alpha+1

color(blue)(= Right Hand Side