If `phi="tan"^(-1)(xsqrt(3))/(2k-x)` and `theta="tan"^(-1)(2x-k)/(k sqrt(3))`, then show that one value of `(phi-theta)` is `30^(@)`.

If phi = tan^-1 (xsqrt3)/(2k-x) and theta (2x-k)/(ksqrt3) , then show that one value of (phi - theta) is 30^@

If phi=cot^(-1)sqrt(cos2theta)-tan^(-1)sqrt(cos2theta) , then show that, sin phi=tan^(2)theta .

If 0 lt theta lt (pi)/(2) and sin ""(theta)/(2)=sqrt((x-1)/(2x)), then the value of tan theta is-

If int tan^(-1)x dx=xtan^(-1)x+k log(1+x^(2))+C , then the value of k is-

If tan theta = (2x - K)/(K sqrt3) " and " tan varphi = (xsqrt3)/(2 K-x), "then show that" |varphi - theta| = 30^(@).

If (1+ tan theta) (1+ tan phi)=2, then the value of (theta+ phi) is

If sec theta -tan theta =(1)/(sqrt(3)) , then determine the values of both sec theta and tan theta.

If (d)/(dx)(tan^(-1)x)^(2)=k tan^(-1)x*(1)/(1+x^(2)) , then the value of k is -

If f(x)=tan^(-1)((3x-x^(3))/(1-3x^(2))) and phi(x)=cos^(-1)((1-x^(2))/(1+x^(2))) , then the value of lim_(x to a) (f(x)-f(a))/(phi(x)-phi(a))(0 lt a lt (1)/(2)) is -