plz answer asap. its based on pure trignometry.
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Answer:
1. -1/8
Step-by-step explanation:
= sin(5π/14) sin(3π/14) sin(π/14)
converting all into cos.
= cos(π/2-5π/14) cos(π/2-3π/14) cos(π/2-π/14)
= cos (2π/14) cos (4π/14) cos(6π/14)
= cos π/7 cos 2π/7 cos 3π/7
= - cos π/7 cos 2π/7 cos 4π/7
now multiply and divide with 2sin π/7
= - [(2 sin π/7 cos π/7)cos 2π/7 cos 4π/7] /2sin π/7
we know that sin2a = 2 sina Cosa
= - (sin 2π/7 cos 2π/7 cos 4π/7 )/ 2sin π/7
= -(sin4π/7 cos4π/7)/4 sin π/7
= - (sin 8π/7)/ 8 sinπ/7
= - sin(π +π/7) / 8 sin π/7
= - sin (π/7)/ 8 sin π/7
= -1/8
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