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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.
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