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# PROVE THAT COS 20.COS80.COS60.COS40=1/16 AND EXPLAIN IT.

Nishant Vora IIT Patna
4 years ago
cos 20`cos 40`cos 60`cos 80` *(8sin 20`/8 sin20`)
=[4 (2 sin 20`cos 20`)cos 40`cos 60`cos 80`]/8 sin20`
= [2 (2 sin 40`cos 40`)cos 60`cos 80`]/8 sin20`
=[(2 sin 80`cos 80`)cos 60`]/8 sin20`
= [(sin 160) (1/2)]/8 sin20` = (1/2)/8 = 1/16

sin 2a = 2 sin a cos a , sin (180 - a) = sin a
Vinesh
11 Points
3 years ago
1/2 (cos 20 cos 40 cos 80)1/2 cos 20 (cos 40 cos 80)1/4 cos 20 ( 2cos 40 cos 80)1/4 cos 20 ( cos (40+80) + cos (40 -80))1/4 cos 20 ( cos 120 + cos 40)-1/8 cos 20 +1/4 (cos 20 cos 40)_1/8 cos 20 +1/8 ( cos 60 + 20 )-1/8 cos 20 + 1/16 +1/8 cos 201/8 (-cos 20 +1/2 + cos 20 )1/16