Question

prove that cos40×cos80×cos160=(-1/8)​

Answer 1

Answer:

Step-by-step explanation: HII!! Its pretty lengthy but i covered all the required steps .

= (1/2) (2 cos 40.cos 80).cos 160

= (1/2) ( cos(40+80) + cos(40 - 80) ).cos 160 { 2cosAcosB = cos(A + B) + cos(A - B) }

= (1/2) ( cos(120) + cos(-40) ).cos 160

= (1/2) ( -1/2 + cos(40) ).cos 160 { cos(-A) = cos(A) }

= (1/2) ( -cos(160)/2 + cos(160)cos(40) )

= (1/2) ( -cos(160)/2 + (1/2)2*cos(160)cos(40) )

= (1/2) ( -cos(160)/2 + (1/2) [ cos(200) + cos(120) ] )

= (1/2) ( -cos(160)/2 + cos(200)/2 + cos(120)/2 )

= (1/2) ( -cos(160)/2 + cos(200)/2 - 1/4 )

= (1/2) ( 1/2 [cos(200) - cos(160)] - 1/4 )

= (1/2) ( 1/2 [-2sin(180)*sin(20))] - 1/4 ) { cos(A)-cos(B)= -2(sin(A+B)/2)*(sin(A-B)/2) }

= (1/2) ( 0 - 1/4 ) { sin(180) = 0 }

= -1/8

HOPE IT WAS HELPFUL !! PLZZ VOTE