Review the important identity:

\[
\cos x \cos y = \frac{1}{2} [\cos(x+y) + \cos(x-y)]
\]

cos x cosy = 2 1 ​ [ cos ( x + y ) + cos ( x − y ) ] R = 2 1 ​ ( cos x cosy − s in x s in y + cos x cosy − s in x s in y ) = 2 1 ​ ⋅ 2 cos x cosy = cos x cosy = L R = L

Answered by Anonymous | 2024-06-10

cos(x+y) = cosxcosy - sinxsiny; cos(x-y) = cosxcosy + sinxsiny; .................................................. => cos(x+y) + cos(x-y) = 2cosxcosy => cosx cosy = 1/2 [cos(x+y) + cos(x−y)];

Answered by crisforp | 2024-06-10

The identity cos x cos y = 2 1 ​ [ cos ( x + y ) + cos ( x − y )] relates the product of cosines to the sum and difference of angles. It can be derived by using known cosine identities and is useful in various mathematical applications. Understanding this identity assists in solving problems involving trigonometric functions effectively.
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Answered by Anonymous | 2024-11-07