Question

if tana + cota/tana - cota = 2 then find the the value of sin a​

Answer 1

$\large\underline{\sf{Solution-}}$

Given Trigonometric equation is

$\rm :\longmapsto\:\dfrac{tana + cota}{tana - cota} = 2$

$\rm :\longmapsto\:tana + cota = 2tana - 2cota$

$\rm :\longmapsto\:tana - 2tana = - cota - 2cota$

$\rm :\longmapsto\: - tana = - 3cota$

$\rm :\longmapsto\: tana = 3cota$

$\rm :\longmapsto\: tana = \dfrac{3}{tana}$

$\rm :\longmapsto\: {tan}^{2}a = 3$

$\rm :\longmapsto\:tana = \sqrt{3}$

$\rm :\longmapsto\:tana = tan60 \degree \:$

$\rm \implies\:a \: = \: 60\degree$

Hence,

$\red{\rm :\longmapsto\:sina = sin60\degree = \dfrac{ \sqrt{3} }{2} \: }$

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$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf Trigonometry\: Table \\ \begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\boxed{\begin{array}{ |c |c|c|c|c|c|} \bf\angle A & \bf{0}^{ \circ} & \bf{30}^{ \circ} & \bf{45}^{ \circ} & \bf{60}^{ \circ} & \bf{90}^{ \circ} \\ \\ \rm sin A & 0 & \dfrac{1}{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} &1 \\ \\ \rm cos \: A & 1 & \dfrac{ \sqrt{3} }{2}& \dfrac{1}{ \sqrt{2} } & \dfrac{1}{2} &0 \\ \\ \rm tan A & 0 & \dfrac{1}{ \sqrt{3} }&1 & \sqrt{3} & \rm \infty \\ \\ \rm cosec A & \rm \infty & 2& \sqrt{2} & \dfrac{2}{ \sqrt{3} } &1 \\ \\ \rm sec A & 1 & \dfrac{2}{ \sqrt{3} }& \sqrt{2} & 2 & \rm \infty \\ \\ \rm cot A & \rm \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } & 0\end{array}}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$