Express the product as a sum containing only sines or cosines.cos (4 ) cos (8 )
Question
Express the product as a sum containing only sines or cosines.cos (4 ) cos (8 )
Solution
The product of cos(4) and cos(8) can be expressed as a sum containing only sines or cosines using the product-to-sum identities in trigonometry. The relevant identity here is:
cos(A)cos(B) = 1/2[cos(A - B) + cos(A + B)]
Applying this identity to the given expression, we get:
cos(4)cos(8) = 1/2[cos(4 - 8) + cos(4 + 8)] = 1/2[cos(-4) + cos(12)] = 1/2[cos(4) + cos(12)]
So, cos(4)cos(8) can be expressed as 1/2[cos(4) + cos(12)].
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