Question

√(3) / sin(40) + 1 / cos(40)

помогите решить, срочно

Answer 1

√(3) / sin(40) + 1 / cos(40) =
=(√(3)*cos(40) + 1* sin(40) )/ (sin(40)*cos(40))=
=4*(√(3)/2*cos(40) + 1/2* sin(40) )/ (sin(40)*cos(40)+sin(40)*cos(40))=
=4*(√(3)/2*cos(40) + 1/2* sin(40) )/ (cos(50)*cos(40)+(sin(40)*sin(50))=
=4*(cos(30)*cos(40) + sin(30)* sin(40) )/ (cos(50)*cos(40)+(sin(40)*sin(50))=
=4*(cos(30-40))/ (cos(50-40)
=4*(cos(-10))/ (cos(10)=4

Answer 2

$frac{ sqrt{3} }{sin40} + frac{1}{cos40} = frac{ sqrt{3}*cos40+1*sin40}{sin40*cos40} =$$frac{ frac{sqrt{3} }{2} *cos40+ frac{1}{2}*sin40}{ frac{1}{4} *2sin40cos40} =$$frac{ sin60 *cos40+ cos60*sin40}{ frac{1}{4} sin80}= frac{sin(60+40)}{frac{1}{4}sin80}$=$frac{sin100}{frac{1}{4}sin80} =frac{sin(90+10)}{frac{1}{4}sin(90-10)}= frac{cos10}{frac{1}{4}cos10}=4$

Answer 3

спасибо большое