If `x=sqrt(7+4sqrt(3)),` prove that`x+1//x=4`

y=sin^(-1)[sqrt(x-a x)-sqrt(a-a x)] then prove that 1/(2sqrtx sqrt(1-x))

If 1/(sqrt(2))

If f(x)=sqrt(4-x^2)+sqrt(x^2-1) , then the maximum value of (f(x))^2 is ____________

If f(x)=sqrt(4-x^2)+sqrt(x^2-1) , then the maximum value of (f(x))^2 is ____________

(1)/(sqrt(x+3)-sqrt(x-4))

If x=7+4sqrt3 then find the value of x+(1)/(x)

If sqrt(sqrt(sqrt(x)))= (( (x^4+4) ^(1/4))^(1/4)) ^(1/4) then the value of x^4 is____.

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)

If sqrt(1-x^6)+sqrt(1-y^6)=a(x^3-y^3), then prove that (dy)/(dx)=(x^2)/(y^2)sqrt((1-y^6)/(1-x^6))

Solve sqrt(x+3-4sqrt(x-1))+sqrt(x+8-6sqrt(x-1))=1