Grade 11Trigonometry
tanθ + tan2θ + √3 tanθ tan2θ = √3 Find tanθ ? Please help.
tanθ + tan2θ + √3 tanθ tan2θ = √3 Find tanθ ? Please help.
2 Answers
Sreevignesh
I can't insert theta so.... I am using x instead of theta
Tan x+tan 2x+ √3 tan x tan 2x =√3
Tan x + tan 2x = √ 3- √3 tan x tan 2 x.
Tan x +tan 2 x= √3(1-tan x tan 2x)
√3. = (tan x+ tan 2x)/(1-tan x tan 2 x)
√3 = tan ( x+2x). [Tan (x+2x)=(tan x+ tan 2x)/(1-tan x tan 2x)]
√3 = tan 3 x
3x. = tan ^-1 ( √3)
3x. = π/3
x. = π/9
Now, tan x = tan π/9
= tan 20° = 0.3639
Kyra
Take root 3tantheta tan 2theta to the right hand side and then take root 3 common and then bring 1+tan theta tan2theta in denominator then tan3theta is equal to root 3.
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