Question #480b6

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Answer 1 · 2016-08-12T16:24:56

#1#

Use #sin x = cos (pi/2-x), cos x = sin (pi/2-x)#,

#tan x = cot (pi/2-x) and cot x = tan(pi/2-x)#.

Also, use #f^(-1)f(X)=X.#

The given expression is

#(sin^(-1)sin(pi/2-x)+cos^(-1)sin(pi/2-x))/(tan^(-1)tan(pi/2-x)+cot^(-1)cot(pi/2-x))#

#=((pi/2-x)+(pi/2-x))/((pi/2-x)+(pi/2-x))#

#=1#

Here, as #x to pi/2#, the limit is also 1..