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Question

Find the value of cos (pi/13) × cos(2pi/13) × cos (3pi/13) × cos (4pi/13) × cos (5pi/13) × cos ( 6pi/13) (A) 1/64 (B) -1/64 (C) 1/32 (D) -1/8

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Solution

Given equation is, cosπ13cos2π13cos3π13cos4π13cos5π13cos6π13Now multiply and divide by 2sinπ13=2sinπ13cosπ13cos2π13cos3π13cos4π13cos5π13cos6π132sinπ13Since sin2a=2sinacosa we get, =sin2π13cos2π13cos3π13cos4π13cos5π13cos6π132sinπ13=2sin2π13cos2π13cos3π13cos4π13cos5π13cos6π1322sinπ13=2sin4π13cos4π13cos3π13cos5π13cos6π1323sinπ13=sin8π13cos3π13cos5π13cos6π1323sinπ13Now divide and multiply by 2sin3π13=2sin3π13cos3π13cos5π13cos6π13sin8π13 24sinπ13 sin3π13=2sin6π13cos6π13sin8π13cos5π13 25sinπ13 sin3π13=sin12π13sin8π13cos5π13 25sinπ13 sin3π13=sinπ-π13sinπ-5π13cos5π13 25sinπ13 sin3π13=sinπ13sin5π13cos5π13 25sinπ13 sin3π13=2sin5π13cos5π13 26 sinπ-10π13=sin10π13 26 sin10π13=164=

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