Question

Prove that tan x.tan (π/3 - x). tan ( π/3+ x) = tan 3x​

Answer 1

Answer:

RHS=tan3x

Step-by-step explanation:

tanx. $\frac{tan60-tanx}{1+tan60.tanx}$.$\frac{tanx+tan60}{1-tanx.tan60}$

tanx.$\frac{tan^{2}60-tan^{2}x}{1-tan^{2}x.tan^{2}60 }$

$\frac{3tanx-tan^{3}x}{1-3tan^{2}x }$

=tan3x

Hence proved

Answer 2

Answer:

tanx. \frac{tan60-tanx}{1+tan60.tanx}1+tan60.tanxtan60−tanx .\frac{tanx+tan60}{1-tanx.tan60}1−tanx.tan60tanx+tan60

tanx.\frac{tan^{2}60-tan^{2}x}{1-tan^{2}x.tan^{2}60 }1−tan2x.tan260tan260−tan2x

\frac{3tanx-tan^{3}x}{1-3tan^{2}x }1−3tan2x3tanx−tan3x

=tan3x

Hence proved