Proving 3 ( sin ⁡ x − cos ⁡ x ) 4 + 4 (...

ScommaMaruj

ScommaMaruj

Answered

2022-07-06

Proving 3 ( sin x cos x ) 4 + 4 ( sin 6 x + cos 6 x ) + 6 ( sin x + cos x ) 2 = 13

Answer & Explanation

iskakanjulc

iskakanjulc

Expert

2022-07-07Added 18 answers

3 ( sin ( x ) cos ) 4 + 4 ( sin 6 x + cos 6 x ) + 6 ( sin x + cos x ) 2 = 13 3 ( ( sin x cos x ) 2 ) 2 + 4 ( sin 2 x + cos 2 x ) ( sin 4 x sin 2 x cos 2 x + cos 4 x ) + 6 ( sin 2 x + 2 sin x cos x + cos 2 x ) = 13 3 ( sin 2 x 2 sin x cos x + cos 2 x ) 2 + 4 ( sin 4 x sin 2 x cos 2 x + cos 4 x ) + 6 ( 1 + sin 2 x ) = 13 3 ( 1 sin 2 x ) 2 + 4 ( ( sin 2 x + cos 2 x ) 2 3 sin 2 x cos 2 x ) + 6 ( 1 + sin 2 x ) = 13 3 ( 1 sin 2 x ) 2 + 4 ( 1 3 sin 2 x cos 2 x ) + 6 ( 1 + sin 2 x ) = 13 3 ( 1 sin 2 x ) 2 + 4 ( 1 3 4 sin 2 2 x ) + 6 ( 1 + sin 2 x ) = 13 3 6 sin 2 x + 3 sin 2 2 x + 4 3 sin 2 x + 6 + 6 sin 2 x = 13
So :
13=13

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