`sin^(-1)sin((3x^(2)-1)/(2x^(2)+2))lt(3)/(4) if (1) -sqrt((5)/(3))ltxltsqrt((5)/(3))quad (2) -(sqrt(10))/(3)ltxlt(sqrt(10))/(3) (3) -1ltxlt1quad (4) -(sqrt(10))/(4)ltxlt(sqrt(10))/(4)`

y=tan^(-1)""(3x-x^(3))/(2x^(2)-1),-(1)/(sqrt(3))ltxlt(1)/(sqrt(3))

y=tan^(-1)""(3x-x^(3))/(2x^(2)-1),-(1)/(sqrt(3))ltxlt(1)/(sqrt(3))

Find (dy)/(dx) , if y=sin^-1((sqrt(1+x)+sqrt(1-x))/2), -1ltxlt1

Given x, y in R , x^(2) + y^(2) gt 0 . Then the range of (x^(2) + y^(2))/(x^(2) + xy + 4y^(2)) is (a) ((10 - 4 sqrt(5))/(3),(10 + 4 sqrt(5))/(3)) (b) ((10 - 4 sqrt(5))/(15),(10 + 4 sqrt(5))/(15)) (c) ((5- 4 sqrt(5))/(15),(5 + 4 sqrt(5))/(15)) (d) ((20- 4 sqrt(5))/(15),(20 + 4 sqrt(5))/(15))

(1)/(sqrt(11-2sqrt(30)))-(3)/(sqrt(7-2sqrt(10)))-(4)/(sqrt(8+4sqrt(3)))

sin^(-1){cot(sin^(-1)(sqrt((2-sqrt(3))/(4))+cos^(-1)((sqrt(12))/(4))+sec^(-1)sqrt(2))}

The value of sin(1/4sin^(-1)((sqrt(63))/8)) is (a) 1/(sqrt(2)) (b) 1/(sqrt(3)) (c) 1/(2sqrt(2)) (d) 1/(3sqrt(3))

If y=tan^(-1)((3x-x^3)/(1-3x^2)),-1/(sqrt(3))ltxlt1 /(sqrt(3)), then find (dy)/(dx)

If y=tan^(-1)((3x-x^3)/(1-3x^2)),-1/(sqrt(3))ltxlt1 /(sqrt(3)), then find (dy)/(dx)

sin ^(-1)[cot ((sin ^(-1) sqrt((2-sqrt(3))/(4)))+cos ^(-1) (sqrt(12))/(4)+sec ^(-1) sqrt(2))]