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#