Compare-it-1-sin-10-cos-10-and-1-

Question Number 160373 by HongKing last updated on 28/Nov/21

Compare it :

\frac{1 - \sin (10 °)}{\cos (10 °)} and 1

Answered by ghimisi last updated on 28/Nov/21

\frac{s i n 90 - s i n 10}{c o s 10} = \frac{2 s i n 40 c o s 50}{s i n 80} =

\frac{2 s i n 40 s i n 40}{2 s i n 40 c o s 40} = t g 40 < t g 45 = 1

Commented by HongKing last updated on 28/Nov/21

Thank you very much, cool, my dear Ser

Answered by mr W last updated on 29/Nov/21

f (x) = \frac{1 - \sin x}{\cos x}

f (0) = 1

f^{'} (x) = - \frac{1}{1 + \sin x} < 0 f o r x < \frac{3 π}{2}

t h a t m e a n s f (x) i s s t r i c t l y d e c r e a s i n g

f o r 0 ⩽ x ⩽ \frac{3 π}{2} . o r

f (x) = \frac{1 - \sin x}{\cos x} < f (0) = 1 f o r a n y x

0 < x ⩽ \frac{3 π}{2} i n c l u d i n g x = 10 °

Commented by HongKing last updated on 29/Nov/21

thank you so much my dear Sir cool