If `(1+4x^(2))cosA=4x,` then show that `"cosec"A+cotA=(1+2x)/(1-2x)`.

Prove that ("cosec"A-cotA)^(2)=((1-cosA))/((1+cosA)).

"cosec"^(-1)((1+x^(2))/(2x))

If cosec A = 4x + (1)/(16x) then cosec A + cot A =

If y = tan ^(-1) ((2x )/( 1 -x ^(2))) + tan ^(-1) ((3x - x ^(3))/( 1 - 3x ^(2)))- tan ^(-1) ((4x - 4x ^(3))/( 1 - 6x + x ^(4))), then show that (dy)/(dx) = (1)/(1 + x ^(2)).

If y = cosec^-1x,x>1 , then show that : x(x^2-1)(d^2y)/(dx^2) + (2x^2-1)(dy)/(dx) = 0

If sin^4x+sin^2x=1 show that, cot^4x+cot^2x=1

If csc theta=x+(1)/(4x) prove that csc theta+cot theta=2x or (1)/(2x)

Prove that (1+cosA)/(1-cosA)=("cosec" A+cotA)^(2)

If y = sin^(-1) x^2 sqrt(1 - x^2) + xsqrt(1 - x^4) , show that (dy)/(dx) - (2x)/(sqrt(1 - x^4)) = 1/(sqrt(1 - x^2))

If y=csc^(-1)x,x>1, then show that x(x^(2)-1)(d^(2)y)/(dx^(2))+(2x^(2)-1)(dy)/(dx)=0