Cho tan a + cot a = m. Tính tan3 a + cot3 a theo m.
Giải thích
Ta có:
• tan2 a + cot2 a
= (tan a + cot a)2 − 2tan a.cot a
= m2 − 2.1
= m2 − 2
• tan3 a + cot3 a
= (tan a + cot a)(tan2 a − tan a.cot a + cot2 a)
= m.(m2 − 2 − 1)
= m.(m2 − 3)
= m3 − 3m
Ta có:
• tan2 a + cot2 a
= (tan a + cot a)2 − 2tan a.cot a
= m2 − 2.1
= m2 − 2
• tan3 a + cot3 a
= (tan a + cot a)(tan2 a − tan a.cot a + cot2 a)
= m.(m2 − 2 − 1)
= m.(m2 − 3)
= m3 − 3m