Trigonometry sin^3(x) + cos^3(x) * tan(x)

Question

Let f(x) = sin³x + cos³x (tan x)

 

Show that f(x) = sin x

 

Thank you for your time!

Answer 1

sin³ x + cos³ x tan x

 

= sin³ x + cos³ x sin x / cos x

 

= sin³ x + cos² x sin x

 

= (sin² x + cos² x)sin x

 

= sin x

Answer 2

show sin^3(x)+cos^3(x)tan(x)=sin(x)

sin^3(x)+cos^3(x)(sin[x]/cos[x])=sin(x)

sin^3(x)+cos^2(x)(sin[x])=sin(x)

factor

sin(x)(sin^2[x]+cos^2[x])=sin(x)

sin^2(x)+cos^2(x)=1 is a trig identity

substitute

sin(x)(1)=sin(x)

sin(x)=sin(x)