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Poftethef9t

Poftethef9t

Answered question

2022-06-18

Prove this inequality with trigonometry 9 cos 2 x 10 cos x sin y 8 cos y sin x + 17 1

Answer & Explanation

victorollaa5

victorollaa5

Beginner2022-06-19Added 16 answers

9 cos 2 x 10 cos x sin y 8 cos y sin x + 17 = 9 cos 2 x 2 cos x sin y 8 ( cos x sin y + cos y sin x ) + 17 = 9 cos 2 x 2 cos x sin y 8 sin ( x + y ) + 17 2 8 + 17 7 1
Emanuel Keith

Emanuel Keith

Beginner2022-06-20Added 8 answers

Let u = 9 cos 2 x 10 cos x sin y 8 cos y sin x
As a 2 + b 2 ( a cos v + b sin v ) a 2 + b 2
( 10 cos x ) 2 + ( 8 sin x ) 2 ( 10 cos x sin y + 8 cos y sin x ) ( 10 cos x ) 2 + ( 8 sin x ) 2
u 9 cos 2 x ( 10 cos x ) 2 + ( 8 sin x ) 2 = ( 9 cos 2 x + 16 1 ) 2 17
Now 3 16 1 9 cos 2 x + 16 1 9 + 16 1 = 4
3 2 ( 9 cos 2 x + 16 1 ) 2 4 2

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