Chủ đề này có 1 trả lời

[datkjlop9a2hVvMF]

Biết $tan\alpha +cot\alpha =k$.Tính:
a/$tan^{2}\alpha +cot^{2}\alpha$
b/$tan^{4}\alpha +cot^{4}\alpha$
c/$tan^{6}\alpha +cot^{6}\alpha$
Chứng minh:$\left | k \right |\geq 2$

[N H Tu prince]

Biết $tan\alpha +cot\alpha =k$.Tính:
a/$tan^{2}\alpha +cot^{2}\alpha$
b/$tan^{4}\alpha +cot^{4}\alpha$
c/$tan^{6}\alpha +cot^{6}\alpha$
Chứng minh:$\left | k \right |\geq 2$

a.$tan^2\alpha+cot^2\alpha=(tan\alpha+cot\alpha)^2-2tan\alpha .cot\alpha=k^2-2$
b.$tan^{4}\alpha +cot^{4}\alpha=(tan^2\alpha+cot^2\alpha)^2-2tan^2\alpha .\cot^2\alpha=(k^2-2)^2-2$
c.$tan^{6}\alpha +cot^{6}\alpha=(tan^2\alpha+cot^2\alpha)^3-3(tan^{2}\alpha +cot^{2}\alpha)tan^2\alpha .\cot^2\alpha$
$=(k^2-2)^3-3(k^2-2)$
*$|k|=tan\alpha +cot\alpha=>\frac{sin\alpha}{cot\alpha}+\frac{cos\alpha}{sin\alpha}=\frac{sin^2\alpha +cos^2\alpha}{sin\alpha .cos\alpha}\geq \frac{2.sin\alpha .cos\alpha}{sin\alpha .cos\alpha}=2$