標題:
發問:
Prove the following identity. ( sin 60 sin 30 + sin 50 sin 40)/(sin 60 cos 30 - cos 50 sin 40) = tan 70
最佳解答:
(sin 60 sin 30 + sin 50 sin 40) / (sin 60 cos 30 - cos 50 sin 40) = [(-1/2)(cos 90 - cos 30) + (-1/2)(cos 90 - cos 10)] / {(1/2)(sin 90 + sin 30) - (1/2)[sin 90 + sin (-10)]} = [(cos 30 - cos 90) + (cos 10 - cos 90)] / [(sin 90 + sin 30) - (sin 90 - sin 10)] = (cos 30 + cos 10) / (sin 30 + sin 10) = (2 cos 20 cos 10) / (2 sin 20 cos 10) = cos 20 / sin 20 = sin 70 / cos 70 = tan 70
其他解答:
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Trig. Identity發問:
Prove the following identity. ( sin 60 sin 30 + sin 50 sin 40)/(sin 60 cos 30 - cos 50 sin 40) = tan 70
最佳解答:
(sin 60 sin 30 + sin 50 sin 40) / (sin 60 cos 30 - cos 50 sin 40) = [(-1/2)(cos 90 - cos 30) + (-1/2)(cos 90 - cos 10)] / {(1/2)(sin 90 + sin 30) - (1/2)[sin 90 + sin (-10)]} = [(cos 30 - cos 90) + (cos 10 - cos 90)] / [(sin 90 + sin 30) - (sin 90 - sin 10)] = (cos 30 + cos 10) / (sin 30 + sin 10) = (2 cos 20 cos 10) / (2 sin 20 cos 10) = cos 20 / sin 20 = sin 70 / cos 70 = tan 70
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