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Question Number 144663 by mathdanisur last updated on 27/Jun/21

x \in (0; π) a n d (a; b) r e a l n u m b e r s f i x e d .

F i n d t h e r a n g e o f f u n c t i o n :

g (x) = \frac{(1 + a^{2} + {c o t}^{2} x) \cdot (1 + b^{2} + {c o t}^{2} x)}{1 + {c o t}^{2} x}

Answered by mindispower last updated on 27/Jun/21

(a^{2} + \frac{1}{{s i n}^{2} (x)}) (\frac{1}{{s i n}^{2} (x)} + b^{2}) . {s i n}^{2} (x)

= (a^{2} + \frac{1}{{s i n}^{2} (x)}) (1 + b^{2} {s i n}^{2} (x))

c a u c h y s h w a r t z ⩾ {(a + b)}^{2} m i n

Commented by mathdanisur last updated on 27/Jun/21

a l o t p e r f e c t, b u t a n s w e r ?

Commented by mindispower last updated on 27/Jun/21

[{(a + b)}^{2}, + \infty [

Commented by mathdanisur last updated on 27/Jun/21

t h a n k s S i r