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

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

Free previous-year papers & practice for JEE, NEET and CBSE Boards.

Properties of Inverse Cosine Function, Sum and Difference Formulae for Inverse Trigonometric Functions | PadhAiPro

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TextProperties of Inverse Cosine FunctionSum and Difference Formulae for Inverse Trigonometric Functions

If a = sin⁻¹(√2/2) + cos⁻¹(-1/2) and b = tan⁻¹(√3) - cot⁻¹(-1/√3), then find the value of a + b.

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

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)]

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].

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