Cho tan góc anpha +cot góc anpha =k Tính a) tan ^2 anpha +cot ^2 anpha b) tan ^3 anpha +cot ^3 anpha
2 câu trả lời
a,
$\tan^2\alpha+\cot^2\alpha$
$=(\tan\alpha+\cot\alpha)^2-2\tan\alpha.\cot\alpha$
$=k^2-2$
b,
$\tan^3\alpha+\cot^3\alpha$
$=(\tan\alpha+\cot\alpha)(\tan^2\alpha+\cot^2\alpha-\tan\alpha.\cot\alpha)$
$=k(k^2-2-1)$
$=k(k^2-3)$
Đáp án:
a, =$(tan\alpha+cot\alpha)^{2}$ -2tan$\alpha$cot$\alpha$= $k^{2}$-2.1=$k^{2}$-2
b, a) tan^3 a+ cot^3 a
= (tana+cot a)(tan^2a-tana.cota+cot^2a)
= k( tan^2 (a) +cot^2a -1)
=k( (tana+cota)^2 -2tana.cota - 1)
=k(k^2-2-1)
=k^3-3k