0(CONCEPT BASED)
Using principal value, find the value of cos^(-1)â?¡(cosâ?¡ã??(2 π)/3ã?? )+sin^(-1)â?¡(sinâ?¡ã??(2 π)/3ã?? )
Differentiate tan-1[(√(1+ x^2 ) -1)/x] w.r.t. x
If e^x ã??+eã??^y=e^(x+y), prove that dy/dx + e^(y-x)=0
Differentiate cos^(-1)â?¡ã??((x+ √(1-x^2 ))/√2)ã?? w.r.t. x
If y √(x^2+1)=logâ?¡ã??(√(x^2+1)-x)ã??, then show that (x2 +1 ) dy/dx + xy + 1 = 0
Let y = (log x)x + xx cosx, then find dy/dx
(APPLICATION BASED)
If tan-1a + tan-1b + tan-1c = π/2 ; prove that ab + bc +ca = 1
Prove that 2 tan-1(1/2) + tan-1 (1/7) = sin-1(31/(25√2))
Solve cos-1((x^2-1)/(x^2+1)) + tan-1(2x/(x^2-1)) = 2π/3
If x^p y^q=ã??(x+y)ã??^(p+q), prove that dy/dx=y/x
Find dy/dx, if y = sin^(-1) (2θ/(1+ θ^2 )) and x = tan^(-1) (2θ/(1- θ^2 ))
If y = x sin y, prove that xdy/dx =y/(1-x cos y)
Prove that: 2 tan-1(√((a-b)/(a+b)) tanâ?¡ã??x/2ã??) = ã??cosã??^(-1) ((a cosâ?¡x+b)/(a+b cosâ?¡x ))
Discuss the continuity and differentiability of the function f(x) = |x| + |x+1| in the interval (-1,2)
(HOTS)
Prove that tan (π/4+1/2 cos^(-1) a/b) + tan (π/4-1/2 cos^(-1) a/b) = 2b/a
Solve : sin-16x + sin-16√3 x = - π/2
Differentiate sin^(-1)â?¡ã??((3 x+4 √(1-x^2 ))/5)ã?? w.r.t. x
If x = a (cos θ + log tanθ/2) and y = a sin θ, then find the value of (d^2 y)/dx^2 at θ = π/4
If x = tan(1/a logâ?¡y), then show that(1+x^2 ) (d^2 y)/dx^2 +(2x-a)dy/dx=0
If cos-1x + cos-1y + cos-1z = π, then prove that x2 + y2 + z2 + 2xyz = 1
