Prove thatcos x ≥ 1 − 12x2 and sin x ≥ x − 12x3 for all x ∈ [0, π/2].Hint: Use the mean value theorem
Question
Solution 1
Sure, let's prove these inequalities step by step.
- Prove that cos x ≥ 1 - 1/2x^2 for all x ∈ [0, π/2].
We start by considering the function f(x) = cos(x) - (1 - 1/2x^2) on the interval [0, π/2]. We want to show that f(x) ≥ 0 for all x in this interval.
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