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Evaluate the following limit: lim(x->pi/...

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

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`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`
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Knowledge Check

  • lim_(x to pi//4)(1- tan x)/(1-sqrt(2) sin x) equals:

    A
    `1/sqrt(2)`
    B
    `1/2`
    C
    `1/(2sqrt(2))`
    D
    1

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