limx->pi/4 {tan(x)-1}/(pi-4x)(adsbygoogle = window.adsbygoogle || []).push({});

I tried to solve it like this:

lim x->pi/4 tan(pi-4x)=

lim x->pi/4 tan(pi-5x+x)

= limx->pi\4 {tanx+tan(pi-5x)}/{1-tan(pi-5x)tanx}

Now

lim x->pi/4 tan(pi-4x)=(pi-4x)

Therefore,

lim x->pi/4 (pi-4x)= lim x->pi/4 (tan(x)-1)/2 [Valid as lim fx/gx=limfx/limgx and lim (fx-gx)=limfx-limgx]

hence

lim x->pi/4 {tan(x)-1}/{pi-4x}=2

But this is wrong

the answer is 1/2

Could someone please point out the mistake in my procedure

Isnt the statement lim x->a (fx -gx)=lim x->a fx-1 where g(a)=1 coorect?

Thanks

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