Question

Tan2A= cot(A -24) Find it na!!!

Answer 1

$\bf\dag$QueStion :

If Tan2A = cot(A -24) then find the value of "A"

$\bf\dag$AnswEr :

$\underline{\bigstar\:\textsf{According \: to \: the \: question:-}}$

$\scriptsize\sf{\: \: \: \: \: \:\:( \green{ Tan(90^{\circ} - A) \: = \: cotA })}$

$\normalsize\hookrightarrow\sf\ cot(90^{\circ} - 2A) \: = \: cot(A - 24^{\circ}) \\ \\ \normalsize\hookrightarrow\sf\cancel{cot}(90^{\circ} - 2A) \: = \: \cancel{cot}(A -24^{\circ}) \\ \\ \normalsize\hookrightarrow\sf\ 90^{\circ} + 24^{\circ} = A + 2A \\ \\ \normalsize\hookrightarrow\sf\ 114^{\circ} = 3A \\ \\ \normalsize\hookrightarrow\sf\ A =\frac{\cancel{114}}{\cancel{3}} = 38^{\circ} \\ \\ \normalsize\hookrightarrow\sf\ A = 38^{\circ}$

$\large\hookrightarrow{\underline{\boxed{\sf\green{A = 38^{\circ}}}}}$

Answer 2

$\huge\mathbb{SOLUTION}$

$\bold{Tan\: 2A\: =\: Cot(A-24)}$

$\bold{Cot(90-2A)\: =\: Cot(A-24)}$

$\bold{90-2A\: =\: A\: -\: 24}$

$\bold{90\: +\: 24\: =\: 2A\: +\: A}$

$\bold{114\: =\: 3A}$

$\bold{A\: =\: 38}$