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Question
Evaluate:
sin 40° sin 50° – cos 40° cos 50°
Evaluate
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Solution
Given: sin 40° sin 50° – cos 40° cos 50°
Step-wise calculation:
1. Use the identity cos (A + B) = cos A cos B – sin A sin B.
2. Rearrange the expression:
sin 40° sin 50° – cos 40° cos 50°
= –(cos 40° cos 50° – sin 40° sin 50°)
= –cos (40° + 50°)
3. Compute the angle:
–cos(90°) = –0
= 0
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