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Sin(A+B)Sin(A-B)

Prove that: 2...

Question

Prove that: $2 \cos x \cos y = \cos (x + y) + \cos (x - y)$

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Solution

In $2 \cos x \cos y = \cos (x + y) + \cos (x - y)$ ,
Taking $R . H . S .$ we have,
$R . H . S . = \cos (x + y) + \cos (x - y)$ ….. $(i)$
By trigonometric identities, we can write;
$\cos (x + y) = \cos x \cos y - \sin x \sin y$
$\cos (x - y) = \cos x \cos y + \sin x \sin y$
Therefore putting these values in $e q (i)$ , we get,
$R . H . S . = (\cos x \cos y - \sin x \sin y) + (\cos x \cos y + \sin x \sin y)$
$= 2 \cos x \cos y$
$= L . H . S .$
Hence, it is proved that $2 \cos x \cos y = \cos (x + y) + \cos (x - y)$ .

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Sin(A+B)Sin(A-B)

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