How do you find the value of $csc [arctan (\frac{x}{\sqrt{2}})]$ $csc [arctan(x/sqrt2)]$ ?

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Answer 1 · 2016-11-11T23:40:37

$csc [arctan (\frac{x}{\sqrt{2}})]$ $csc [arctan(x/sqrt2)]$

$= csc [a r c cot (\frac{\sqrt{2}}{x})]$ $=csc [arc cot(sqrt2/x)]$

$= csc ⎡ ⎢ ⎣ a r c csc \sqrt{1 + {(\frac{\sqrt{2}}{x})}^{2}} ⎤ ⎥ ⎦$ $=csc [arc cscsqrt(1+(sqrt2/x)^2)]$

$= \sqrt{1 + {(\frac{\sqrt{2}}{x})}^{2}}$ $=sqrt(1+(sqrt2/x)^2)$

$= \sqrt{1 + \frac{2}{x^{2}}}$ $=sqrt(1+2/x^2)$

$= \frac{\sqrt{x^{2} + 2}}{x}$ $=sqrt(x^2+2)/x$

How do you find the value of csc [arctan(x/sqrt2)]csc[arctan(x√2)]csc [arctan(x/sqrt2)]?