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Erin Lozano 2022-06-24 Answered
Solve the following equation: sin 14 x + cos 14 x = 169 64 cos 6 2 x
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Answers (1)

Paxton James
Answered 2022-06-25 Author has 25 answers
2 sin 2 x = 1 cos 2 x 2 cos 2 x = 1 + cos 2 x 128 ( sin 14 x + cos 14 x ) = ( 1 cos 2 x ) 7 + ( 1 + cos 2 x ) 7 = 2 ( 1 + 21 cos 2 2 x + 35 cos 4 2 x + 7 cos 6 2 x ) 169 cos 6 2 x = 1 + 21 cos 2 2 x + 35 cos 4 2 x + 7 cos 6 2 x 0 = 162 cos 6 2 x 35 cos 4 2 x 21 cos 2 2 x 1 0 = ( 2 cos 2 2 x 1 ) ( 81 cos 4 2 x + 23 cos 2 2 x + 1 ) cos 2 2 x = 1 2 or 23 ± 23 2 4 ( 81 ) 2 ( 81 ) < 0
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