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" If "f(x)={[sin^(-1)(sin x),x>0],[(pi)/...

" If "f(x)={[sin^(-1)(sin x),x>0],[(pi)/(2),,x=0],[cos^(-1)(cos x),,x<0]

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If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

If f(x)={{:(sin(cos^(-1)x)+cos(sin^(-1)x)",",xle0),(sin(cos^(-1)x)-cos(sin^(-1)x)",",xgt0):} then at x = 0

f_(1)(x)=sin^(-1)(cos(sin^(2)x)),f_(2)(x)=cos^(-1)(sin(cos^(2)x)),f_(3)(x)=sin^(-1)(cos^(2)x)),f_(4)(x)=cos^(-1)(sin^(2)x)* Then which of the following is/are correct?

f(x)=1+2sin x+3cos^(2)x,0<=x<=(2 pi)/(3)

Find the area bounded by the curves y=(sin^(-1)(sin x)+cos^(-1)(cos x)) and y=(sin^(-1)(sin x)+cos^(-1)(cos x))^(2) for 0<=x<=2 pi