Question

Find the coordinates of midpoint of line joining the points (sin 45,tan 30),(cos 45,cot 60)

Answer 1

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Answer 2

$Let \: A( sin 45 \degree, tan 30 \degree ) = ( x_{1} , y_{1} ) \\ and \: B( cos 45 \degree, cot 30 \degree ) = ( x_{2} , y_{2} )$

$We \: know \:that ,$

$Mid \: point \: of \: line \: segment \: AB \\= \Big ( \frac{ x_{1} + x_{2} }{2} , \frac{ y_{1} + y_{2} }{2}\Big)$

$= \Big( \frac{ sin 45 \degree + cos 45 \degree}{2} ,\frac{ tan 30 \degree + cot 60 \degree}{2} \Big) \\= \Big( \frac{ \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}}{2} , \frac{ \frac{1}{\sqrt{3}} + \frac{1}{\sqrt{3}}}{2} \Big) \\= \Big( \frac{\frac{2}{\sqrt{2}}}{2} , \frac{\frac{2}{\sqrt{3}}}{2} \Big ) \\= \Big( \frac{2}{2\sqrt{2}} , \frac{2}{2\sqrt{3}} \Big ) \\= \Big( \frac{1}{\sqrt{2}} , \frac{1}{\sqrt{3}} \Big )$

Therefore.,

$\red{ Mid \:point \: of \: line \: joining \:the }\\\red{ points \: ( sin 45 \degree, tan 30 \degree )\: and \: ( cos 45 \degree, cot 30 \degree ) }$

$\green { = \Big( \frac{1}{\sqrt{2}} , \frac{1}{\sqrt{3}} \Big )}$

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