M2 Q. Tri. function 快 20分!

2011-02-28 12:04 pm
Q. Prove that tan 2A + 2 cotA=tan2Acot^2A

回答 (2)

2011-02-28 4:46 pm
✔ 最佳答案
tan 2A + 2 cot A

= 2 tan A/(1 - tan2 A) + 2/tan A

= [2 tan2 A + 2(1 - tan2 A)]/[tan A(1 - tan2 A)]

= 2/[tan A(1 - tan2 A)]

= [2 tan A/(1 - tan2 A)] x cot2 A

= tan 2A cot2 A
參考: 原創答案
2011-02-28 4:48 pm
Sol
tan2A+2cotA
=1/cot2A + cot^2A-1/cot2A
=cot^2A/cot2A
=cot^2A*tan2A


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