साबित करें कि: tan^(-1) [ (sqrt(1+z) +sqrt(1-z))/(sqrt(1+z) -sqrt(1-z))]= pi/4+1/2 cos^(-1) z |...

Prove that : tan^(-1) [ (sqrt(1+z) +sqrt(1-z))/(sqrt(1+z) -sqrt(1-z))] = pi/4 +1/2 cos^(-1) z

If e^(x)=(sqrt(1+z)-sqrt(1-z))/(sqrt(1+z)+sqrt(1-z)) and tan (y/2)=sqrt((1-z)/(1+z)) then the value of (dy)/(dx) at z=1 is equal to to

Show : sqrt( x^-1y) times sqrt( y^-1z ) times sqrt( z^-1x) = 1

If sin^(-1)x + sin^(-1)y + sin^(-1)z =pi , prove that xsqrt(1 - x^(2)) + y sqrt(1 -y^(2)) + z sqrt(1-z^(2))= 2xyz .

If sin ^ (- 1) x + sin ^ (- 1) y + sin ^ (- 1) z = pi, Prove x sqrt (1-x ^ (2)) + y sqrt (1-y ^ (2) ) + z sqrt (1-z ^ (2)) = 2xyz

If x=int_(0)^(t^(2))e^(sqrt(z)){(2tan sqrt(z)+1-tan^(2)sqrt(z))/(2sqrt(z)sec^(2)sqrt(z))}dz and x=int_(0)^(t^(2))e^(sqrt(z)){(1-tan^(2)sqrt(z)-2tan sqrt(z))/(2sqrt(z)sec^(2)sqrt(z))}dz : Then the inclination of the tangent to the curve at t=(pi)/(4) is :

If sqrt(x+1)+sqrt(y)+sqrt(z-4)=(x+y+z)/(2), then find x+y+z

If x, y, z are distinct positive real numbers is A.P. then (1)/(sqrt(x)+sqrt(y)), (1)/(sqrt(z)+sqrt(x)), (1)/(sqrt(y)+sqrt(z)) are in