Question

tan theta/2 = cot2theta find theta

Answer 1

Answer:

$\sf{The \ value \ of \ \theta \ is \ 51^\circ15'45"}$

Given:

$\sf{\leadsto{\dfrac{tan\theta}{2}=cot^{2}\theta}}$

To find:

$\sf{The \ value \ of \ \theta.}$

Solution:

$\sf{\leadsto{\dfrac{tan\theta}{2}=cot^{2}\theta}}$

$\sf{But, \ cot\theta=\dfrac{1}{tan\theta}}$

$\sf{\leadsto{\dfrac{tan\theta}{2}=\dfrac{1}{tan^{2}\theta}}}$

$\sf{\leadsto{tan^{3}\theta=2}}$

$\sf{\leadsto{tan\theta=\sqrt[3]{2}}}$

$\sf{\leadsto{\theta=tan^{-1}(\sqrt[3]{2})}}$

$\sf{By \ using \ log \ table}$

$\sf{\leadsto{\theta=tan^{-1}(1.260)}}$

$\sf{\leadsto{\theta=51^\circ15'45"}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ \theta \ is \ 51^\circ15'45"}}}$