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Question:

The value of sec⁻¹(1/4Σₖ=₀¹⁰sec(7π/12 + kπ/2)sec(7π/12 + (k+1)π/2)) in the interval [-π/4, 3π/4] equals

0.00

Solution:

Correct option is A. 0.00
Evaluate sec⁻¹[1/4Σₖ=₀¹⁰sec(7π/12 + kπ/2)sec(7π/12 + (k+1)π/2)]
Given exp = sec⁻¹[1/4Σₖ=₀¹⁰(7π/12 + kπ/2)cosec(7π/12 + kπ/2)] = sec⁻¹[1/4Σₖ=₀¹⁰2sin(7π/6 + kπ)] = sec⁻¹[1/2Σₖ=₀¹⁰(-1)ᵏ⁺¹sin(π/6)] = sec⁻¹(Σₖ=₀¹⁰(-1)ᵏ⁺¹/2) = sec⁻¹(1/2) = 0