y-tgx-ctgx-8-0-pi-2-Find-min-y-

Question Number 207361 by hardmath last updated on 12/May/24

y = \frac{tg x + ctg x}{8}, (0; \frac{π}{2})

Find : \min (y) = ?

Answered by Berbere last updated on 12/May/24

c t g (x) = \frac{1}{y}; y = t a n (x)

\Leftrightarrow M i n (\frac{1}{8} (y + \frac{1}{y}); y \in] 0, \infty [)

y + \frac{1}{y} ⩾ 2 \sqrt{y . \frac{1}{y}} = 2

m i n (\frac{1}{8} (y + \frac{1}{y})) ⩾ \frac{2}{8} = \frac{1}{4};

e q u a l i t y x = \frac{π}{4}

Commented by hardmath last updated on 12/May/24

thank you very much dear professor cool

Commented by Berbere last updated on 13/May/24

w i t h e p l e a s u r i m n o t p r o f e s s o r

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