Question

If tan 15= 2- root3, then the value of cot square 75 is

Answer 1

$\Huge \purple {\underline {\overline {\mathbb {ANSWER:}}}}$

$\huge \pink {\underline {\mathbb {GIVEN:}}}$

$\Large \purple {\tt {\tan(15) = 2 - \sqrt{3}}}$

$\huge \pink {\underline {\mathbb {EXPLANATION:}}}$

$\Large \purple {\tt {~~ {\cot(75)}^{2} = {\tan(90-75)}^{2}}}$

$\Large \pink {\tt {\implies {\tan(15)}^{2}}}$

$\Large \purple {\tt {\implies {(2- \sqrt{3})}^{2}}}$

$\Large \pink {\tt {\implies {2}^{2} - 2(2)(\sqrt{3}) + {\sqrt{3}}^{2} }}$

$\Large \purple {\tt {\implies 4 - 4 \sqrt{3} + 3}}$

$\Large \pink {\tt {\implies 4 + 3 - 4 \sqrt{3}}}$

$\Large {\tt \purple {\implies 7 - 4 \sqrt{3}}}$

$\huge \pink {\mathbb {\underline {FORMULA~USED:}}}$

$\Huge \purple {\tt {\underline {Identity~II:}}}$

$\large \purple {\boxed {\tt \pink {{(a-b)}^{2} = {a}^{2} - 2(a)(b) + {b}^{2}}}}$