If `tan^-1 x=A,` then prove that ` sec A=sqrt(1+x^2)`

If y= tan^-1 x then prove that (1+x^2) y_(2) + 2xy_(1) =0. Differentiate sec^-1(1/(2x^2 -1)) with respect to sqrt 1-x^2 .

If cos^(-1)x+2sin^(-1)x+3cot^(-1)y+4tan^(-1)y=4sec^(-1)z+5cos ec^(-1)z, then prove that sqrt(z^(2)-1)=(sqrt(1+x^(2))-xy)/(x+y sqrt(1-x^(2)))

Prove that tan^(-1) x =sec^(-1) sqrt(1+x^2)

If tan^(-1)(1+x)+tan^(-1)(1-x)=(pi)/(6), then prove that x^(2)=2sqrt(3).

Prove : tan^-1x=sec^-1sqrt(1+x^2) .

If sec?+tan?=x, prove that sin?=x2-1

if sec A=x+(1)/(4x) then prove that sec A+tan A=2x,(1)/(2x)

If sec theta=x+(1)/(4x), then prove that sec theta+tan theta=2x or (1)/(2x)

If tan^(-1).(a+x)/(a) + tan ^(-1) ((a-x)/(a)) = (pi)/(6) then prove that x^(2) = 2sqrt(3)a^(2)

If tan^(-1).(a+x)/(a) + tan ^(-1) ((a-x)/(a)) = (pi)/(6) then prove that x^(2) = 2sqrt(3)a^(2)