What is the value of the expression [ 1 + cos ⁡ ( π 8...

aangenaamyj

aangenaamyj

Answered

2022-07-02

What is the value of the expression [ 1 + cos ( π 8 ) ] [ 1 + cos ( 3 π 8 ) ] [ 1 + cos ( 5 π 8 ) ] [ 1 + cos ( 7 π 8 ) ]?

Answer & Explanation

Lana Schwartz

Lana Schwartz

Expert

2022-07-03Added 8 answers

( 1 + cos ( π 8 ) ) ( 1 + cos ( 3 π 8 ) ) ( 1 + cos ( 5 π 8 ) ) ( 1 + cos ( 7 π 8 ) ) = = ( 1 + cos ( π 8 ) ) ( 1 + cos ( 3 π 8 ) ) ( 1 + cos ( π 3 π 8 ) ) ( 1 + cos ( π π 8 ) ) = = ( 1 + cos ( π 8 ) ) ( 1 + cos ( 3 π 8 ) ) ( 1 cos ( 3 π 8 ) ) ( 1 cos ( π 8 ) ) = = ( 1 cos 2 π 8 ) ( 1 cos 2 3 π 8 ) = sin 2 π 8 sin 2 3 π 8 = ( 1 cos π 4 ) 2 ( 1 cos 3 π 4 ) 2 = = ( 1 cos π 4 ) ( 1 cos ( π π 4 ) ) 4 = ( 1 cos π 4 ) ( 1 + cos π 4 ) 4 = 1 cos 2 π 4 4 = 1 1 2 4 = 1 8

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