sin^(-1)((sqrt(1+x)+sqrt(1-x))/(2))

If y=sin^(-1)(xsqrt(1-x)+sqrt(x)sqrt(1-x^2)) and (dy)/(dx)=1/(2sqrt(x(1-x)))+p , then p is equal to 0 (b) 1/(sqrt(1-x)) sin^(-1)sqrt(x) (d) 1/(sqrt(1-x^2))

(d)/(dx)[sin^(-1)(xsqrt(1 - x)- sqrt(x)sqrt(1 - x^(2)))] is equal to

Prove that tan^(-1)((sqrt(1+x)-sqrt(1-sin x))/(sqrt(1+x)-sqrt(1-sin x)))=(pi)/(4)-(1)/(2)cos^(-1),-(1)/(sqrt(2))<=x<=1

Prove that sin^(-1)(frac[sqrt(1+x)+sqrt(1-x)][2])=frac[pi][4]+frac[1][2]cos^(-1)x,0ltxlt1

cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2)

If f(x)=sin^(-1)(sqrt(3)/2x-1/2sqrt(1-x^(2))), -1/2 le x le 1 , then f(x) is equal to

If x in[(sqrt(3))/(2), 1] then [sin^(-1){(x)/(sqrt(2))+(sqrt(1-x^(2)))/(sqrt(2))}-sin^(-1)x]=

Prove that : cot^(-1)(sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x))=(x)/(2),0

int_(0)^(1)sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))dx

(d)/(dx)[sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))] is