Question

Find
the co-ordinates of
mid point of line
the points
(sin45°, tan 30°), (Cos 45°,cot 60°)​

Answer 1

$Let \: A(sin 45\degree, tan 30\degree)= ( x_{1} , y_{1}) ,\\B( cos 45\degree,cot 60\degree) = ( x_{2} , y_{2})$

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

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

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

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

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

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

Therefore.,

$\red{Coordinates \: of \: Mid \: point \: of}\\\red{ joining \: of \: points \: (sin 45\degree, tan 30\degree) }\\\red{and \:(cos 45\degree,cot 60\degree)} \green { = \Big( \frac{1}{\sqrt{2}} , \frac{1}{\sqrt{3}}\Big)}$

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