Can't figure out this Trig. proof: cos &#x2061;<!-- ⁡ --> ( x + y ) cos

Caleb Proctor 2022-07-04 Answered
Can't figure out this Trig. proof: cos ( x + y ) cos ( x y ) = cos 2 ( x ) sin 2 ( y )
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Answers (1)

sniokd
Answered 2022-07-05 Author has 22 answers
HINT: Notice,
L H S = cos ( x + y ) cos ( x y ) = ( cos x cos y sin x sin y ) ( cos x cos y + sin x sin y )
= ( cos x cos y ) 2 ( sin x sin y ) 2
= cos 2 x cos 2 y sin 2 x sin 2 y
= cos 2 x ( 1 sin 2 y ) ( 1 cos 2 x ) sin 2 y
= cos 2 x cos 2 x sin 2 y sin 2 y + cos 2 x sin 2 y
= cos 2 x sin 2 y

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