If `a in (0,1)a n df(a)=(a^2-a+1)+(8sin^2a)/(sqrt(a^2-a+1))+(27 cos e c^2a)/(sqrt(a^2-a+1))` , then the least value of `(f(a))/2` is_______

If cos 2theta=(sqrt(2)+1)(cos theta-(1)/(sqrt(2))) , then the general value of theta(n in Z)

f(2)(sqrt(1-cos x))^(2)=(sin x)^(2)

sin^(-1)(-(sqrt(3))/(2))+cos^(-1)((sqrt(3))/(2))

1. sin^(-1) (1/sqrt2) 2. cos^(-1) (sqrt3/2)

1. sin^(-1) (1/sqrt2) 2. cos^(-1) (sqrt3/2)

If the value of the definite integral int_(0)^(1)(sin^(-1)sqrt(x))/(x^(2)-x+1)dx is (pi^(2))/(sqrt(n)) (where n in N), then the value of (n)/(27) is

lim_(x rarr0)(sin^(2)x)/(sqrt(2)-sqrt(1+cos x))=(A)sqrt(2)(B)2(C)

sin ^ (- 1) a-cos ^ (- 1) b = sin ^ (- 1) (ab-sqrt (1-a ^ (2)) sqrt (1-b ^ (2)))

If 0ltAltBltpi, sin A-sinB=(1)/(sqrt2) and cos A-cos B=sqrt((3)/(2)) , then the value of A+B is equal to