How Solve function?

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1 Answer
Dec 16, 2017

See below.

Explanation:

I'm not sure if this is the right expression. I can't make out properly what the denominator of the first fraction is, it looks like #ctg#.

Using identities:

#color(red)(cotx =cosx/sinx)#

#color(red)(sin^2x+cos^2x=1)#

#lim_(x->pi/2)(sinx/cotx-1/cosx)#

#sinx/cotx=sinx/(cosx/sinx)=sin^2x/cosx#

#sin^2x/cosx-1/cosx=(sin^2x-1)/cosx#

#sin^2x=1-cos^2x#

#((1-cos^2x)-1)/cosx=-cos^2x/cosx=-cosx#

#:.#

#-cos(pi/2)=0#

So:

#lim_(x->pi/2)(sinx/cotx-1/cosx)=0#