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dokezwa17 2022-05-24 Answered
If sin x + sin 2 x = 1 then find the value of cos 8 x + 2 cos 6 x + cos 4 x
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Answers (2)

bgu999dq
Answered 2022-05-25 Author has 9 answers
sin x + sin 2 x = 1
sin x = 1 sin 2 x
sin x = cos 2 x
Now
cos 8 x + 2 cos 6 x + cos 4 x
= sin 4 x + 2 sin 3 x + sin 2 x
= sin 4 x + sin 3 x + sin 3 x + sin 2 x
= sin 3 x ( sin x + 1 ) + sin 2 x ( sin x + 1 )
( sin x + 1 ) ( sin 3 x + sin 2 x ) = ( sin x + 1 ) ( sin x + 1 ) sin 2 x = ( sin 2 x + sin x ) ( sin 2 x + sin x ) = 1
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Angel Malone
Answered 2022-05-26 Author has 1 answers
Even shorter:
You know sin x = cos 2 x. Then
cos 8 x + 2 cos 6 x + cos 4 x = sin 4 x + 2 sin 3 x + sin 2 x = ( sin 2 x + sin x ) 2 = 1 2 = 1
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