What does $cos(arctan(2))+sin(arcsec(1))$ equal?

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Answer 1 · 2016-09-30T23:58:54

$cos(arctan(2)) + sin(arcsec(1)) = sqrt(5)/5$

Consider the right angled triangle with sides $1, 2, sqrt(5)$ ...

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Then:

$tan alpha = "opposite"/"adjacent" = 2/1 = 2$

and

$cos alpha = "adjacent"/"hypotenuse" = 1/sqrt(5) = sqrt(5)/5$

So:

$cos(arctan(2)) = sqrt(5)/5$

Note also that:

$sec(0) = 1/cos(0) = 1/1 = 1$

$sin(0) = 0$

So we find:

$sin(arcsec(1)) = sin(0) = 0$

Putting it together:

$cos(arctan(2)) + sin(arcsec(1)) = sqrt(5)/5$

What does cos(arctan(2))+sin(arcsec(1))cos(arctan(2))+sin(arcsec(1)) equal?