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$