limit x tends to π/2 x/cosecx
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Explanation:
y=x->π/2[(cosecx - 1)/(π/2 -x)²]
This is of the form 0/0.
y=x->π/2[(-cosecxcotx)/[2(π/2 - x)(-1)]
Cancelling -1
y=x->π/2[(cosecxcotx)/(π-2x)]
y=x->π/2[((1/sinx)(cosx/sinx))/(π-2x)]
y=x->π/2[(cosx)/(sin²x(π-2x))]
y=x->π/2[(sin(π/2 - x)/(sin²x.(π-2x))]
y=x->π/2[(sin(π/2 - x))/(2sin²x(π/2 - x))]
Ltx->π/2[(sin(π/2 - x))/(π/2 - x)]=1
y=1/(2sin²(π/2))
y=1/(2(1)²)
y=1/2
Hope this helps.........
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