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Given cos 120° - cos 40° = 2 sin(C+D)/2 sin(C-D)/2

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Answer

−2sin⁡80∘sin⁡40∘-2 \sin 80^\circ \sin 40^\circ

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यहाँ दिए गए प्रश्न का हल है:

समस्या: cos⁡120∘−cos⁡40∘\cos 120^\circ - \cos 40^\circ को साइन और कोसाइन के गुणनफल के रूप में व्यक्त करें।

  1. योग को गुणनफल में बदलने के लिए सूत्र का उपयोग करें।

    हम सूत्र cos⁡C−cos⁡D=−2sin⁡(C+D2)sin⁡(C−D2)\cos C - \cos D = -2 \sin \left(\frac{C+D}{2}\right) \sin \left(\frac{C-D}{2}\right) का उपयोग करेंगे।
    यहाँ, C=120∘C = 120^\circ और D=40∘D = 40^\circ है।

  2. CC और DD के मानों को सूत्र में प्रतिस्थापित करें।

    cos⁡120∘−cos⁡40∘=−2sin⁡(120∘+40∘2)sin⁡(120∘−40∘2)\cos 120^\circ - \cos 40^\circ = -2 \sin \left(\frac{120^\circ+40^\circ}{2}\right) \sin \left(\frac{120^\circ-40^\circ}{2}\right)

  3. कोष्ठकों के अंदर के मानों को सरल करें।

    =−2sin⁡(160∘2)sin⁡(80∘2)= -2 \sin \left(\frac{160^\circ}{2}\right) \sin \left(\frac{80^\circ}{2}\right)

  4. कोणों को सरल करें।

    =−2sin⁡(80∘)sin⁡(40∘)= -2 \sin (80^\circ) \sin (40^\circ)

    अंतिम उत्तर है:

    −2sin⁡80∘sin⁡40∘-2 \sin 80^\circ \sin 40^\circ
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