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infogus88

infogus88

Answered question

2022-05-21

Prove that cos 6 β sin 6 β = 1 16 ( 15 cos 2 β + cos 6 β )

Answer & Explanation

bshizzey7h

bshizzey7h

Beginner2022-05-22Added 9 answers

( cos 2 β ) 3 ( sin 2 β ) 3 = ( cos 2 β sin 2 β ) ( cos 4 β + sin 4 β + cos 2 β sin 2 β )
= cos 2 β ( 1 sin 2 β cos 2 β )
= cos 2 β ( 1 sin 2 2 β 4 )
= cos 2 β ( 1 + cos 4 β 1 8 )
Now use 2 cos A . cos B = cos ( A + B ) + cos ( A B )
= 1 8 ( 7 cos 2 β + cos 2 β cos 4 β )
= 1 8 ( 7 cos 2 β + cos 6 β + cos 2 β 2 )
= 1 16 ( 15 cos 2 β + cos 6 β )

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