Find the exact solutions to each equation for the interval 0<=x<2pi. tan^3 x + 2tan^2 + tan x=0
tan x (tan^2 +2tan+1)=0 or tanx=0 or (tanx +1)=0 solve it for x
tanx(tan^2x+2tanx+1)=0 tanx=0 tan^2x+2tanx+1=0 tanx=0 => remember tanx=sinx/cosx (so we are looking for where sinx is zero) so x=0, pi ,and 2pi now we also have tan^2x+2tanx+1=0 let u=tanx u^2+2u+1=0 (u+1)(u+1)=0 u+1=0 u=-1 but remember tanx=u tanx=-1 sinx/cosx=-1 we are looking for where sinx and cosx are the opposite so x=3pi/4,7pi/4
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