`y=4x^(2)` and `(x^(2))/(a^2)-(y^2)/(16)=1` intersect if
`|a|le 1/sqrt(2)`
`|a|le -1/sqrt(2)`
`|a|ge 1/sqrt(2)`

If -1 le x le -(1)/sqrt(2) then sin^(-1)2xsqrt(1-x^(2)) equals

If y=(sin^(-1)x cos^(-1)((x^2)/2))/(1+x^2) then find the value of y(1/2) + y(1/sqrt2) + y(-1/2) + y(-1/sqrt2)

Prove that : sin^(-1) (2x sqrt(1-x^(2)))= 2 sin^(-1) x, - 1/(sqrt(2)) le x le 1/(sqrt(2))

Prove that : sin^(-1) (2x sqrt(1-x^(2)) ) = 2 sin^(-1) x , -1/(sqrt(2))le x le 1/(sqrt(2)

Prove that : tan^(-1)((2xsqrt(1-x^(2)))/(1-2x^(2))) =2sin^(- 1)x when : - 1/(sqrt(2)) le x le 1/(sqrt(2))

Equation of a line which is tangent to both the curve y=x^(2)+1 and y=x^(2) is y=sqrt(2)x+(1)/(2) (b) y=sqrt(2)x-(1)/(2)y=-sqrt(2)x+(1)/(2)(d)y=-sqrt(2)x-(1)/(2)

sin ^ (- 1) ((x ^ (2)) / (4) + (y ^ (2)) / (9)) + cos ^ (- 1) ((x) / (2sqrt (2)) + (y) / (3sqrt (2)) - 2)

If x*y=sqrt(x^2+y^2) the value of (1*2 sqrt 2)(1*-2 sqrt 2) is

If sqrt(x) + sqrt(y) = sqrt(a) , then (dy)/(dx) = 1/(2sqrt(x)) + 1/(2sqrt(y)) = 1/(2sqrt(a))

If 0 le x le 2pi , then 2^(cosec^(2) x) sqrt(1/2 y^(2) -y+1) le sqrt(2)