Need to find a 3\cot(x+y) if \tan(x) and \tan(y) are

albusgks

albusgks

Answered question

2022-04-21

Need to find a 3cot(x+y) if tan(x) and tan(y) are the solutions of x235x+2=0

Answer & Explanation

Brianna Sims

Brianna Sims

Beginner2022-04-22Added 19 answers

From quadratic equation given,
tanx+tany=35
tanxtany=2
So by the Compound Angle Formula,
tan(x+y)=tanx+tany1tanxtany=351=35
So we have
3cot(x+y)=31tan(x+y)=3135=55
zavesiljid

zavesiljid

Beginner2022-04-23Added 21 answers

Since by Vieta's formulas one has
tanx+tany=351=35, tanxtany=21
=2
one has
3cot(x+y)=31tan(x+y)=31tanxtanytanx+tany
=3(12)35=55

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