If y = cos⁻¹((1 – x²)/(1 + x²)), 0 < x < 1, then find dy/dx.

Question

TextProperties of Inverse Cosine FunctionCBSE PYQ

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Assertion (A) : cos⁻¹(cos 13π/6) is equal to π/6. Reason (R) : The range of the principal value branch of the function y = cos⁻¹ x is [0, π].

Evaluate : cos⁻¹[cos(-7π/3)]

Principal Value Branch of Inverse Trigonometric Functions

Properties of Inverse Cosine Function

Assertion (A) : cos⁻¹(cos(13π/6)) is equal to π/6. Reason (R) : The range of the principal value branch of the function y = cos⁻¹ x is [0, π].

Simplify : cos⁻¹x + cos⁻¹[x/2 + √(3 – 3x²)/2]; 1/2 ≤ x ≤ 1

cos–1 (1/2) + 2 sin–1 (1/2)

3cos–1 x = cos–1 (4x³ – 3x), x ∈ [1/2, 1]