Question : Evaluate the following.
$\sin 25^{\circ} \sin 65^{\circ}-\cos 25^{\circ} \cos 65^{\circ}$.
Option 1: 40
Option 2: 4
Option 3: 0
Option 4: 1
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Correct Answer: 0
Solution :
$\sin 25^{\circ} \sin 65^{\circ}-\cos 25^{\circ} \cos 65^{\circ}$
We know that,
$\cos(x + y) = \cos x \cos y - \sin x \sin y$
Applying,
$\sin 25^{\circ} \sin 65^{\circ}-\cos 25^{\circ} \cos 65^{\circ}$
= $-(-\sin 25^{\circ} \sin 65^{\circ}+\cos 25^{\circ} \cos 65^{\circ})$
= $-\cos(25^{\circ}+65^{\circ})$
= $-\cos90^{\circ}=0$
Hence, the correct answer is 0.
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