Question

If tan3A=x, tan6A=y, tan 9A= z then

Answer 1

$\textbf{Given:}$

$tan3A=x,\;tan6A=y\;\text{and}\;tan9A=z$

$\textbf{To find:}$

$\text{The relation between x, y and z}$

$\text{We know that,}$

$\boxed{\bf\,tan(A+B)=\dfrac{tanA+tanB}{1-tanA\,tanB}}$

$\implies\,tan9A=tan(3A+6A)$

$tan9A=\dfrac{tan3A+tan6A}{1-tan3A\,tan6A}$

$z=\dfrac{x+y}{1-xy}$

$z(1-xy)=x+y$

$z-xyz=x+y$

$\impies\bf\,x+y+z=xyz$

$\therefore\textbf{The relation betweeen x,y and z is x+y+z=xyz}$

Find more:

यदि A+B+C= 90 तो सिद्ध कीजिए: tanAtanB+tanBtanC+tanCtanA=1

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