1. Given that tan² α - tan² β = 1.
Prove sec² α - sec² β = 1
2. Prove
sin² θ tan θ + cos² θ cot θ + 2 sinθ cosθ = secθ cscθ
MATH M2 Trigonometry Question
2010-03-20 10:27 pm
回答 (1)
2010-03-20 10:45 pm
✔ 最佳答案
1)sec^ 2 A - sec^2 B
=(tan^ 2 A + 1) - (tan^2 B + 1)
=tan^ 2 A - tan^2 B
= 1
2)
LHS
= sin^2θ tanθ + cos^2θ cotθ + 2sinθcosθ
= sin^3θ / cosθ + cos^3θ / sinθ + 2sinθcosθ
= (sin^4θ + cos^4θ) / (sinθ cosθ) + 2sinθcosθ
= (sin^4θ + cos^4θ + 2sin^2θ cos^2θ) / (sinθcosθ)
= (sin^2θ + cos^2θ)^2 / (sinθ cosθ)
= 1 / (sinθ cosθ)
= secθcscθ
= RHS
收錄日期: 2021-04-21 22:10:29
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100320000051KK00766