f(x)= ∫_0 ^( x_ ) e^(t ) (((1+sin t)/(1+cos t))) dt. Then f((π/3))×f(((2π)/3)) = ?


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Question Number 39440 by rahul 19 last updated on 06/Jul/18

$f (x) = \int_{0}^{x_{}} e^{t} (\frac{1 + \sin t}{1 + \cos t}) d t .$ $T hen f (\frac{π}{3}) \times f (\frac{2 π}{3}) = ?$
	Answered by tanmay.chaudhury50@gmail.com last updated on 06/Jul/18

	$f (x) = \int_{0}^{x} e^{t} (\frac{1 + 2 s i n \frac{t}{2} c o s \frac{t}{2}}{2 {c o s}^{2} \frac{t}{2}}) d t$ $= \int_{0}^{x} e^{t} (\frac{1}{2} {s e c}^{2} \frac{t}{2} + t a n \frac{t}{2}) d t$ $= \int_{0}^{x} \frac{d}{d t} (e^{t} t a n \frac{t}{2}) d t$ $=∣ e^{t} t a n \frac{t}{2} ∣_{0}^{x} = e^{x} t a n \frac{x}{2}$ $e^{\frac{Π}{3}} . t a n \frac{Π}{6} . e^{\frac{2 Π}{3}} . t a n \frac{2 Π}{6}$ $e . t a n 30^{o} . t a n 60^{o} = e . \frac{1}{\sqrt{3}} . \sqrt{3} = e$
	Commented by rahul 19 last updated on 06/Jul/18
	Thank you sir . ��
	Commented by tanmay.chaudhury50@gmail.com last updated on 06/Jul/18

	$i t i s r a i n i n g h e a v i l y a t n a g p u r f r o m l a s t n i g h t$ $n o e l e c t r i c t y f r o m m o r n i n g . . . l i f e g e t s t o p p e d$ $. . . m o b i l e b a t t e r y 37 p e r e n t . . . s o b y e . . . r e s u m e$ $a g a i n a f t e r c h a r g i n g . . .$
	Commented by math khazana by abdo last updated on 06/Jul/18

	$u s e a s o l a r c h a r g e r . . . i t s m o s t u s e f u l i n t h i s c a s e . . .$
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