" (v.) "x^(sin x-cos x)+((x^(2)-1)/(x^(2)+1))

("sin x - cos x")^(2) =1- sin 2x

sin[cot^(-1)((2x)/(1-x^(2)))+cos^(-1)((1-x^(2))/(1+x^(2)))]=

((1) / ((sec x) ^ (2) - (cos x) ^ (2)) + (1) / ((cos ecx) ^ (2) - (sin x) ^ (2))) ( cos x) ^ (2) (sin x) ^ (2) = (1- (cos x) ^ (2) (sin x) ^ (2)) / (2+ (cos x) ^ (2) (sin x) ^ (2))

{ cos (sin ^(-1) x)}^(2) ={sin (cos ^(-1) x)}^(2)

(1 + sin x-cos x) / (1 + sin x + cos x) = tan ((x) / (2))

(1+sin x+cos x)^(2)=2(1+sin x)(1+cos x)

(cos^(3) x- sin^(2) x)/(cos x - sin x)=(1)/(2) (2 + sin 2x)

Show that cos 2 x=cos ^(2) x-sin ^(2) x=2 cos ^(2) x-1=1-2 sin ^(2) x=(1-tan ^(2) x)/(1+tan ^(2) x)

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?