f-x-0-x-e-t-1-sin-t-1-cos-t-dt-Then-f-pi-3-f-2pi-3-

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 \dots l i f e g e t s t o p p e d

\dots m o b i l e b a t t e r y 37 p e r e n t \dots s o b y e \dots r e s u m e

a g a i n a f t e r c h a r g i n g \dots

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 \dots i t s m o s t u s e f u l i n t h i s c a s e \dots