Evaluate : `int(dx)/(sqrt(1-sinx))`

1.	Evaluate : `int(dx)/(sqrt(1-sinx))`
Answer» `int(dx)/(sqrt(1-sinx))=(dx)/([sin^(2)(x//2)+cos^(2)(x//2)-2"sin"(x)/(2)"cos"(x)/(2)]^(1//2))` `=int(dx)/(("sin"(x)/(2)-"cos"(x)/(2)))=(1)/(sqrt(2))int(dx)/(((1)/(sqrt(2))"sin"(x)/(2)-"cos"(x)/(2)(1)/(sqrt(2))))` `=(1)/(sqrt(2))int(dx)/(("sin"(x)/(2)"cos"(pi)/(4)-"cos"(x)/(2)"sin"(pi)/(4)))` `=(1)/(sqrt(2))int"cosec"((pi)/(2)-(pi)/(4))dx=(1)/(sqrt(2))2log[tan((x)/(4)-(pi)/(8))]+C` `=sqrt(2)logtan((x)/(4)-(pi)/(8))+C`.

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