Here is the expression: 2 ( sin 6 </msup> &#x2061;<!-- ⁡ --> x + cos

ban1ka1u 2022-07-12 Answered
Here is the expression:
2 ( sin 6 x + cos 6 x ) 3 ( sin 4 x + cos 4 x ) + 1
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Answers (2)

1s1zubv
Answered 2022-07-13 Author has 17 answers
sin 4 x + cos 4 x = ( sin 2 x + cos 2 x ) 2 2 sin 2 x cos 2 x = 1 2 sin 2 x cos 2 x
sin 6 x + cos 6 x = ( sin 2 x + cos 2 x ) 3 3 sin 2 x cos 2 x ( sin 2 x + cos 2 x ) = 1 3 sin 2 x cos 2 x
Thus your expression simplifies to
2 6 sin 2 x cos 2 x 3 + 6 sin 2 x cos 2 x + 1
Which is 0, for all x

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Desirae Washington
Answered 2022-07-14 Author has 5 answers
2 ( sin 6 x + cos 6 x ) 3 ( sin 4 x + cos 4 x ) + 1 =
= 2 ( sin 2 x + cos 2 x ) ( sin 4 x sin 2 x cos 2 x + cos 4 x ) 3 ( sin 4 x + cos 4 x ) + 1 =
= 2 ( sin 4 x sin 2 x cos 2 x + cos 4 x ) 3 ( sin 4 x + cos 4 x ) + 1 =
= 2 sin 2 x cos 2 x sin 4 x cos 4 x + 1 =
( sin 2 x + cos 2 x ) 2 + 1 = 1 + 1 = 0

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