Prove that cos 2pie/15 × cos 4pie/15 × cos 8pie/15 × cos 16pie/15 = 1/16
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Step-by-step explanation:
cos215πcos415πcos815πcos1415π=116
=−cosπ15cos215πcos415πcos815π
=cosAcos2Acos22A....cosAnA=sin2nA2nsinA
A=π15
=−cosAcos2Aco22Acos23A
=−sin24(1615π)24sin(π16)
=−sin(1615π)16sin(π15)
=−−sinπ1516sinπ15
cos215πcos415πcos815πcos1415π=116.
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