`sin^-1(1/2)` is equal to

the value of cos(cos^-1x+sin^-1(x-2)) is equal to (A) 0 (B) 1 (C) -1 (D) sqrt(1-x^2).sqrt(x^2-4x+3) +x (x-2)

If 0 < x <1, then sqrt(1+x^2)[{xcos(cot^-1x)+sin(cot^-1 x)}^2-1]^(1/2) is equal to

int(1)/(1+3 sin ^(2)x)dx is equal to

The value of sin^-1 (sqrt(3)/2)+ sin^-1 (1/sqrt(2)) is equal to (A) sin^-1 ((sqrt(3+1))/(2sqrt(2))) (B) pi-sin^-1 ((sqrt(3+1))/(2sqrt(2))) (C) pi+sin^-1 ((sqrt(3+1))/(2sqrt(2))) (D) none of these

The valueof 2sin^(-1).(4)/(5)+2sin^(-1).(5)/(13)+2sin^(-1).(16)/(65) is equal to

The value of sin^(-1) (sin 12) + cos^(-1) (cos 12) is equal to

If f(x)=sin^(-1)""(2*(3)^(x))/(1+9^(x)) , then f'(-(1)/(2)) is equal to

The value of lim_(nrarrinfty) ("sin"(pi)/(2n)."sin"(2pi)/(2n)."sin"(3pi)/(2n)..."sin"((n-1)pi)/(2n))^(1//n) is equal to

The value of the definite integral I=int_(-1)^(1)ln((2-sin^(3)x)/(2+sin^(3)x))dx is equal to

Let A=[(1,3cos 2theta,1),(sin2theta, 1, 3 cos 2 theta),(1, sin 2 theta, 1)] the maximum value of |A| is equal to k, then (k-3)^(2) is equal to