हल करें `tan x+tan2x+tan 2x=0`

Explanation

प्रश्न से `tanx+tan2x+tan(x+2x)=0`
या `tanx+tan2x+(tanx+tan2x)/(1-tanx tan2x)=0`
या `(tanx+tan2x)(1+(1)/(1-tanx tan2x))=0`
`:. tan theta +tan2x=0` या `1+(1)/(1-tanx tan2x)=0`
जब `tanx +tan2x=0` तो `tan 2x=-tanx`
या `tan2x=tan(-x):. 2x=npi+(-x)`
या `3x, n pi, " " :. x=(npi)/(3)`
पुनः यदि `1+(1)/(1-tan x tan 2x)=0` तो `2-tanx tan2x=0`
या `tanx tan2x=2,` या `tanx(2tanx)/(1-tan^(2)x)=2`
या `tan^(2)=1-tan^(2)x` या `2tan^(2)x=1`
या `tan^(2)x=(1)/(2)`
या `tanx=pm(1)/(sqrt(2))=pmtan alpha` जहाँ `tan theta =(1)/(sqrt(2))`
या `tanx=tan(pm alpha)`
`:.x=npi+alpha` जहाँ `alpha=tan^(-1)((1)/(sqrt(2))), x =(npi)/(3), n in Z`