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To evaluate the expression ( sin 25° sin 65° – cos 25° cos 65° ), we can use the sine subtraction identity, which states that:
[
sin A sin B – cos A cos B = -cos(A + B)
]
In this case, let ( A = 25° ) and ( B = 65° ). Then we have:
[
sin 25° sin 65° – cos 25° cos 65° = -cos(25° + 65°)
]
Calculating ( 25° + 65° ):
[
25° + 65° = 90°
]
Now, substituting back into the expression:
[
-cos(90°)
]
We know that ( cos(90°) = 0 ):
[
-cos(90°) = -0 = 0
]
Thus, the value of the expression ( sin 25° sin 65° – cos 25° cos 65° ) is:
[
boxed{0}
]