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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

Grade:10

2 Answers

Arun
25763 Points
3 years ago

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........

Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

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

Thanks and Regards

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