.已知∠A、∠B、∠C是△ABC内角,求证：tanA/2 * tanB/2 + tanB/2 * tanC/2 + tanC/2 _数学解答

.已知∠A、∠B、∠C是△ABC内角,求证：tanA/2 * tanB/2 + tanB/2 * tanC/2 + tanC/2 * tanA/2 = 1
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人气：230 ℃　时间：2019-10-29 20:25:47

解答

tanA/2×tanB/2+tanB/2×tanC/2+tanC/2×tanA/2 =tanA/2×tanB/2+tanC/2×(tanA/2+tanB/2) =tanA/2×tanB/2+tan[90-(A+B)/2]×(tanA/2+tanB/2) =tanA/2×tanB/2+cot(A/2+B/2)×(tanA/2+tanB/2) =tanA/2×tanB/2+(tan...