Find the value of tan100tan190+tan110tan200+tan120tan210+...+tan170tan260
without using a calculator.
Please show steps!
Thanks very much!!!!!!
F4 Maths trigonometry(20marks)
2010-05-18 1:38 am
回答 (1)
2010-05-18 2:08 am
✔ 最佳答案
tan 100 = tan (90 + 10) = -1/tan 10tan 190 = tan (180 + 10) = tan 10
so tan 100 tan 190 = (-1/tan 10)( tan 10) = -1.
Similarly, tan 110 tan 200 = tan ( 90 + 20) tan (180 + 20) = (- 1/tan 20)( tan 20) = - 1.
From 100 to 170, there are 8 terms, so answer is - 8.
收錄日期: 2021-04-25 22:38:29
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