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一、因忽视直角三角形而出错例1在ΔABC中,∠A、∠B、∠C的对边为a、b、c,且a:b:c=3:4:5.求证:sinA+sinB=7/5.错证设a=3k,b=4k,c=5k,则sinA=a/c=(3k)/(5k)=3/5,sinB=b/c=(4k)/(5k)=4/5.∴sinA+sinB=3/5+4/5=7/5.剖析由于题中并没有说明∠C=90°,因此直接运用正弦、余弦函数的定义是不全面的.应先证明ΔABC为直角三角形且∠C=90°后,才能运用定义证明结论的正确.
First, due to neglect of right-angled triangle error Example 1 In ΔABC, 对A, ∠B, 对C on the opposite side of a, b, c, and a: b: c = 3: 4: = 7/5. If a = 3k, b = 4k and c = 5k, sinA = a / c = 3k / 5k = 3/5 and sinB = b / c = 4k / 5k) = 4 / 5.sinA + sinB = 3/5 + 4/5 = 7 / 5.According to the title does not explain ∠C = 90 °, so the direct use of sine, the definition of the cosine function is not comprehensive It should be proved that ΔABC is a right triangle and ∠C = 90 °, then the definition can be used to prove the conclusion is correct.