Prove that cos π / 15 . cos 2 π / 15 . cos 3 π / 15 . cos 4 π / 15 . cos 5 π / 15 . cos 6 π / 15 . cos 7 π / 15 = 1/ 2^7
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Answered by
6
Answer:
It's too easy
cos(π/15) .cos(2π/15) .cos(3π/15) .cos(4π/15) .cos(5π/15) .cos(6π/15) .cos(7π/15)
=cos(π/15) .cos(2π/15) .cos(π- 12π/15) .cos(4π/15) .cos(π/3) .cos(6π/15) .cos(π-8π/15)
={cos(π/15) .cos(2π/15) .cos(4π/15) .cos(π-8π/15) }.{cos(π/3)}.{cos(6π/15).cos(8π/15)}
use the formula
=-1/24 * 1/2 * -1/22
=1/27
Answered by
0
Answer:
Step-by-step explanation:
It's too easy
cos(π/15) .cos(2π/15) .cos(3π/15) .cos(4π/15) .cos(5π/15) .cos(6π/15) .cos(7π/15)
=cos(π/15) .cos(2π/15) .cos(π- 12π/15) .cos(4π/15) .cos(π/3) .cos(6π/15) .cos(π-8π/15)
={cos(π/15) .cos(2π/15) .cos(4π/15) .cos(π-8π/15) }.{cos(π/3)}.{cos(6π/15).cos(8π/15)}
use the formula
=-1/24 * 1/2 * -1/22
=1/27
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