" 717.If "Delta(x)=|[1,cos x,1-cos x],[1+sin x,cos x,1+sin x-cos x],[sin x,sin x,1]|" then "int_(0)^((pi)/(2))Delta(x)dx" is equal to- "

If Delta (x)=|{:(1,cos x,1-cos x),(1+sin x,cos x,1+sinx-cosx),(sinx,sinx,1):}| then int_(0)^(pi//2)Delta(x) dx is equal to

If Delta (x)=|{:(1,cos x,1-cos x),(1+sin x,cos x,1+sinx-cosx),(sinx,sinx,1):}| then int_(0)^(pi//2)Delta(x) dx is equal to

If Delta (x)=|{:(1,cos x,1-cos x),(1+sin x,cos x,1+sinx-cosx),(sinx,sinx,1):}| then int_(0)^(pi//2)Delta(x) dx is equal to

If Delta (x)= |(1,cos x,1-cos x),(1+sin x ,cos x,1+sin x-cos x),(sin x,sin x,1)| , then int_(0)^(pi//2) Delta (x) dx= a) (-1)/(2) b) (1)/(2) c)1 d) -1

int(sin x cos x)/(1+sin x+cos x)

(cos x)/(1-sin x)=(1+cos x+sin x)/(1+cos x-sin x)

int(cos 2x)/(1+sin x cos x)dx

int(cos x+sin x)/(cos x-sin x)(1-sin2x)dx

int_(0)^( pi/2)(sin x)/(1+cos x)dx

If y = |{:(sin x , cos x , sin x),(cos x,-sin x, cos x),(x, 1, 1):}| , then (dy)/(dx) is