Prove that ,for any acute angle α secα cosecα +tanα +cotα ≥4.


Question and Answers Forum

All Questions Topic List
None Questions
Previous in All Question Next in All Question
Previous in None Next in None
Question Number 8105 by 314159 last updated on 30/Sep/16

$P r o v e t h a t, f o r a n y a c u t e a n g l e α$ $s e c α c o s e c α + t a n α + c o t α ⩾ 4 .$
Commented by Yozzia last updated on 30/Sep/16

$f (x) = \frac{1}{c o s x s i n x} + \frac{s i n x}{c o s x} + \frac{c o s x}{s i n x}$ $f (x) = \frac{1}{c o s x s i n x} + \frac{1}{s i n x c o s x}$ $f (x) = \frac{2}{c o s s i n x} = \frac{4}{s i n 2 x} = 4 c o s e c 2 x$ $S i n c e 0 < α < 90 ° \Rightarrow 0 < 2 α < 180 °$ $\Rightarrow 0 < s i n 2 x ⩽ 1 \Rightarrow c o s e c 2 x ⩾ 1$ $\Rightarrow 4 c o s e c 2 x ⩾ 4 \Rightarrow f (x) ⩾ 4$ $∴ s e c x c o s e c x + t a n x + c o t x ⩾ 4 \forall x \in (0, 90 °) .$
	Answered by prakash jain last updated on 02/Oct/16

	$answer in coments$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum