Help with this question please on trig!!?

Question

sin^3(x)-2cos^3(x)=0

i get about three lines down on my paper and i still end up with a sin(x) with all cos(x) or vice versa.

Please help me!

Thank you!

Answer 1

sin^3(x)-2cos^3(x)=0

Or sin^3(x) = 2cos^3(x)

Or sin^3(x)/cos^3(x) = 2

Or tan^3(x) = 2

Or tan(x) = 2^(1/3) = 1.26

Or x = atan{1.26} = 51.56 deg

Answer 2

sin³x - 2cos³x = 0

sin³x = 2cos³x

sin³x / cos³x = 2

(sinx / cosx = tanx)

sin³x / cos³x = tan³x

tan³x = 2

(tanx)³ = 2

tanx = 2^1/3

x = 51°34'