Question:
\(\sin 60^{\circ} - \sin 80^{\circ} + \sin 100^{\circ} - \sin 120^{\circ} =\)
\(\sin 60^{\circ} - \sin 80^{\circ} + \sin 100^{\circ} - \sin 120^{\circ} =\)
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\(\sin(180^{\circ} - \theta) = \sin \theta\).
Updated On: Apr 25, 2026
- \(\sqrt{3}\)
- \(\frac{\sqrt{3} + 1}{2}\)
- \(2\sqrt{3}\)
- \(\frac{\sqrt{3}}{4}\)
- 0
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The Correct Option is
Solution and Explanation
Step 1: Understanding the Concept:
Use \(\sin(180^{\circ} - \theta) = \sin \theta\) and \(\sin(120^{\circ}) = \sin 60^{\circ}\).
Step 2: Detailed Explanation:
\(\sin 100^{\circ} = \sin(180^{\circ} - 80^{\circ}) = \sin 80^{\circ}\)
\(\sin 120^{\circ} = \sin(180^{\circ} - 60^{\circ}) = \sin 60^{\circ}\)
So expression becomes: \(\sin 60^{\circ} - \sin 80^{\circ} + \sin 80^{\circ} - \sin 60^{\circ} = 0\)
Step 3: Final Answer:
The value is 0.
Use \(\sin(180^{\circ} - \theta) = \sin \theta\) and \(\sin(120^{\circ}) = \sin 60^{\circ}\).
Step 2: Detailed Explanation:
\(\sin 100^{\circ} = \sin(180^{\circ} - 80^{\circ}) = \sin 80^{\circ}\)
\(\sin 120^{\circ} = \sin(180^{\circ} - 60^{\circ}) = \sin 60^{\circ}\)
So expression becomes: \(\sin 60^{\circ} - \sin 80^{\circ} + \sin 80^{\circ} - \sin 60^{\circ} = 0\)
Step 3: Final Answer:
The value is 0.
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