How do you simplify the expression #tan(arcsin(x/5)) #?

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Answer 1 · 2016-08-01T12:05:57

#x/sqrt(25-x^2)#

Let #a = arc sin (x/5) in [-pi/2, pi/2]#

Then, #sin a =x/5 in [-1, 1]#, and so, #x in [-5, 5]#,

Now, the given expression is

#tan a#

# = sin a/cos a#

#=sin a/sqrt(1-sin^2a)#

#=(x/5)/sqrt(1-(x/5)^2)#
#=x/sqrt(25-x^2)#