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bandikizaui 2022-07-04 Answered
If tan ( α ) + cot ( α ) = p ,, denote tan 3 ( α ) + cot 3 ( α ) in terms of p
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Answers (1)

Nicolas Calhoun
Answered 2022-07-05 Author has 15 answers
Let u = tan ( α )
Solu tion #1: u + 1 u = p ( u + 1 u ) 2 = p 2 u 2 + 1 u 2 = p 2 2 u 2 u ( 1 u ) + 1 u 2 = p 2 3 ( u + 1 u ) ( u 2 u ( 1 u ) + 1 u 2 ) = p ( p 2 3 ) u 3 + ( 1 u ) 3 = p ( p 2 3 ) Solu tion #2: u + 1 u = p ( u + 1 u ) 3 = p 3 u 3 + 3 u 2 ( 1 u ) + 3 u ( 1 u ) 2 + ( 1 u ) 3 = p 3 u 3 + 3 ( u + 1 u ) + ( 1 u ) 3 = p 3 u 3 + ( 1 u ) 3 = p 3 3 p

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