Evaluate the following limit: `lim_(x->pi/4)(1-t a n x)/(1-sqrt(2)sin x)`

Explanation

`lim_(x->pi/4)(1-t a n x)/(1-sqrt(2)sin x)`

`=lim_(x->pi/4)(1-t a n x)/(1-sqrt(2)sin x) xx (1+sqrt2sinx)/(1+sqrt2sinx)`

`=lim_(x->pi/4)(1-t a n x)/(1-2sin ^2x) xx (1+sqrt2sinx)/1`

`=lim_(x->pi/4)(1-(sinx)/(cosx))/(cos^2x-sin ^2x) xx (1+sqrt2sinx)/1`

`=lim_(x->pi/4)(1/(cosx(cosx+sinx)))xx (1+sqrt2sinx)/1`

`=2`