What is the value of the expression [ 1 + cos &#x2061;<!-- ⁡ --> ( &#x03C0;<!--

aangenaamyj

aangenaamyj

Answered question

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

Beginner2022-07-03Added 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?