U have to Prove that: cos π/7 *cos 2π/7 *cos 3π/7 =1/8
Nikhil2412pandey , 6 Years ago
Grade 12
Trigonometry> U have to Prove that: cos π/7 *cos 2π/7 *...
1 Answers
Arun
Last Activity: 6 Years ago
Dear student
A = cos 3π/7. cos 2π/7. cos π/7
cos 3π/7 = cos 6π/14 = cos ( π - 8π/14 ) = - cos 8π/14
Then,
A = - cos 8π/14. cos 4π/14. cos 2π/14
= - cos x. cos 2x. cos 4x, ... x = 2π/14
= (-1/ 2 sin x ). ( 2 sin x. cos x ). cos 2x. cos 4x
= (-1/ 4 sin x ). ( 2 sin 2x. cos 2x ). cos 4x
= (-1/ 8 sin x ). ( 2 sin 4x. cos 4x )
= (-1/8). ( 1 / sin x ). sin 8x
= (-1/8). ( 1/ sin π/7 ). sin 8π/7
= (-1/8). ( 1/ sin π/7 ). sin ( π + π/7)
= (-1/8). ( 1/ sin π/7 ). ( - sin π/7 )
= 1/8
cos 3π/7 = cos 6π/14 = cos ( π - 8π/14 ) = - cos 8π/14
Then,
A = - cos 8π/14. cos 4π/14. cos 2π/14
= - cos x. cos 2x. cos 4x, ... x = 2π/14
= (-1/ 2 sin x ). ( 2 sin x. cos x ). cos 2x. cos 4x
= (-1/ 4 sin x ). ( 2 sin 2x. cos 2x ). cos 4x
= (-1/ 8 sin x ). ( 2 sin 4x. cos 4x )
= (-1/8). ( 1 / sin x ). sin 8x
= (-1/8). ( 1/ sin π/7 ). sin 8π/7
= (-1/8). ( 1/ sin π/7 ). sin ( π + π/7)
= (-1/8). ( 1/ sin π/7 ). ( - sin π/7 )
= 1/8
Regards
Arun (askIITians forum expert)
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