Prove that: 4 ( cos 4 </msup> &#x20

kokoszzm

kokoszzm

Answered question

2022-06-11

Prove that: 4 ( cos 4 π 8 + cos 4 3 π 8 ) cos 4 7 π 8 cos 4 11 π 8 =

Answer & Explanation

last99erib

last99erib

Beginner2022-06-12Added 19 answers

HINT:
π 8 + 3 π 8 = π 2
So, cos 3 π 8 = sin π 8
Now
cos 4 x + sin 4 x = ( cos 2 x + sin 2 x ) 2 2 cos 2 x + sin 2 x = 1 ( 2 sin x cos x ) 2 2 = 1 sin 2 2 x 2
Similarly, 11 π 8 7 π 8 = π 2
cos 11 π 8 = cos ( π 2 + 7 π 8 ) = sin 7 π 8
Now cos 4 y ( sin y ) 4 = ( cos 2 y sin 2 y ) ( cos 2 y + sin 2 y ) = cos 2 y

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