Math, asked by asmitabaidya18, 5 months ago

Prove that cos 2pie/15 × cos 4pie/15 × cos 8pie/15 × cos 16pie/15 = 1/16

Answers

Answered by pizzaboypizza9000

1

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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