The value of equals to

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

The value of (cos⁡41∘+cos⁡42∘+cos⁡43∘+⋯+cos⁡4179∘)−(\cos^4 1^\circ + \cos^4 2^\circ + \cos^4 3^\circ + \dots + \cos^4 179^\circ) - (sin⁡41∘+sin⁡42∘+sin⁡43∘+⋯+sin⁡4179∘)(\sin^4 1^\circ + \sin^4 2^\circ + \sin^4 3^\circ + \dots + \sin^4 179^\circ) equals to (1) 2cos⁡1∘2 \cos 1^\circ (2) -1 (3) 2sin⁡1∘2 \sin 1^\circ (4) 0

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