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

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Answer 1 · 2017-04-19T06:41:58

see below

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