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cos 20 degree cos 40 degree cos 80 degree =1 upon 8 prove karna hai cos 20 degree cos 40 degree cos 80 degree =1 upon 8 prove karna hai
cos20 cos40 cos80= 1/8l.h.s. :cos20 cos40 cos80 multiply nd divide by 21/2 (2 cos20 cos40 cos80)1/2 (cos(20+80)+ cos(20-80)) cos40 (2cosa cosb= cos(a+b) + cos(a-b))1/2 (cos(-60)+ cos(100)) cos401/2 (1/2 + cos100)cos401/4 cos40+ 1/2 (cos40 cos100)multiplt nd divide by 22/2(1/4 cos40) + 1/4 (2 cos40 cos100)1/4 cos40+ 1/4 (cos140+ cos(-60)) (2cosa cosb= cos(a+b) cos(a-b))1/4 cos40+ 1/4 cos140 + 1/8 (cos60= 1/2)1/4 (cos40+cos140) + 1/81/4(2 cos90 cos(-50)) + 1/8 (as above identity)cos90= 01/8= r.h.shence proved........
cos20 cos40 cos80= 1/8
l.h.s. :
cos20 cos40 cos80
multiply nd divide by 2
1/2 (2 cos20 cos40 cos80)
1/2 (cos(20+80)+ cos(20-80)) cos40 (2cosa cosb= cos(a+b) + cos(a-b))
1/2 (cos(-60)+ cos(100)) cos40
1/2 (1/2 + cos100)cos40
1/4 cos40+ 1/2 (cos40 cos100)
multiplt nd divide by 2
2/2(1/4 cos40) + 1/4 (2 cos40 cos100)
1/4 cos40+ 1/4 (cos140+ cos(-60)) (2cosa cosb= cos(a+b) cos(a-b))
1/4 cos40+ 1/4 cos140 + 1/8 (cos60= 1/2)
1/4 (cos40+cos140) + 1/8
1/4(2 cos90 cos(-50)) + 1/8 (as above identity)
cos90= 0
1/8
= r.h.s
hence proved........
Dear Student,Please find below the solution to your problem.cos20 cos40 cos80= 1/8l.h.s. :cos20 cos40 cos80multiply nd divide by 21/2 (2 cos20 cos40 cos80)1/2 (cos(20+80)+ cos(20-80)) cos40 (2cosa cosb= cos(a+b) + cos(a-b))1/2 (cos(-60)+ cos(100)) cos401/2 (1/2 + cos100)cos401/4 cos40+ 1/2 (cos40 cos100)multiplt nd divide by 22/2(1/4 cos40) + 1/4 (2 cos40 cos100)1/4 cos40+ 1/4 (cos140+ cos(-60)) (2cosa cosb= cos(a+b) cos(a-b))1/4 cos40+ 1/4 cos140 + 1/8 (cos60= 1/2)1/4 (cos40+cos140) + 1/81/4(2 cos90 cos(-50)) + 1/8 (as above identity)cos90= 01/8= r.h.sThanks and Regards
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