The value of `lim_(x rarr pi/4) sqrt(1 - sqrt(sin 2x))/(pi - 4x) is`

Explanation

`lim_(x->pi/4)sqrt(1-sqrt(sin2x))/(pi-4x)`

multiplying and dividing by `sqrt(1+sqrt(sin2x))`

`lim_(x->pi/4)(1^2-sin2x)^(1/2)/(pi-4x(sqrt(1+sqrt(sin2x))`

`lim_(h->0)(1-sin(2(pi/4+h))^(1/2))/((pi-4(pi/4+h))(sqrt1+sqrtsin^2(pi/4+h))`

`lim_(h->0)(1-1+2sin^2h)^(1/2)/(4hsqrt2)`

`lim_(h->0)(2^(1/2)sinh)/(4sqrt2h)`

`1/4`.