If tan^-1( (√(1+x²) - √(1-x²)) / (√(1+x²) + √(1-x²)) ) = α, prove that sin2α = x²

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TextSum and Difference Formulae for Inverse Trigonometric Functions

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Solve for x : 5tan⁻¹x + 3cot⁻¹x = 2π

If tan⁻¹((x-1)/(x+1)) + tan⁻¹((2x-1)/(2x+1)) = tan⁻¹(23/36) then prove that 24x² − 23x − 12 = 0

Sum and Difference Formulae for Inverse Trigonometric Functions

Find the value of tan⁻¹x - cot⁻¹x, if (tan⁻¹x)² - (cot⁻¹x)² = 5π/8

Solve for x: 2tan^-1(1/3) + sec^-1(5√2/7) = tan^-1 x

If cos⁻¹ x/2 + cos⁻¹ y/3 = θ, then prove that 9x² − 12xy cos θ + 4y² = 36 sin² θ