If \tan(x_1) \cdots\tan(x_n)=1 for acute x_i, then does it follow

Swebaceacichegh

Swebaceacichegh

Answered question

2022-01-26

If tan(x1)tan(xn)=1 for acute xi, then does it follow that cos(x1)++cos(xn)n22 ?

Answer & Explanation

Emilie Booker

Emilie Booker

Beginner2022-01-27Added 14 answers

For three variables we can use C-S:
Let tan{x}=ba,  tan{y}=cb, where a, b and c are positives.
Thus, tan{z}=ac and by C-S we obtain:
cyccos{x}=cyc11+tan2x=cycaa+b
cyca(a+b)(a+c)cyc(a+c)32
where the last inequality its

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