Inverse Trigonometry Continuity and Differentiability

If y = (tan^–1x)², show that (x² + 1)² y₂ + 2x(x² + 1)y₁ = 2

If x = a (θ-sinθ), y = a (1+cosθ), find

d²y/dx²

If the function

is continuous at x = 1, find the values of ‘a’ and ‘b’.

If y = cosec^–1 x, x > 1, then show that

Verify Rolle’s theorem for the function

Differentiate the functions:

If

Find the values of a and b such that the function defined by  

Differentiate w.r.t. x

For a positive constant ‘a’ find

If

If

For what value of λ is the function defined by

If

If cosy = xcos (a+y), with cos a≠ ±1, prove that

If x = asin2t(1+cos2t) and y = b cos2t(1-cos2t), show that

If

If

If x = a sint and y = a

If