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Teisingai pasinaudoti pateiktomis formulėmis

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Pasinaudodami e matematikas pateiktomis formulėmis apskaičiuokite  reiškinio    sin35xcos65-cos65cos5-cos55cos5  reikšmę.

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[tex]\sin35^\circ\cos65^\circ-\cos65^\circ\cos5^\circ-\cos55^\circ\cos5^\circ=\dfrac{1}{2}(\sin(35^\circ-65^\circ)+\sin(35^\circ+65^\circ))-\\\dfrac{1}{2}(\cos(65^\circ-5^\circ)+\cos(65^\circ+5^\circ))-\dfrac{1}{2}(\cos(55^\circ-5^\circ)+\cos(55^\circ+5^\circ))=\dfrac{1}{2}(\sin(-30^\circ)+\sin100^\circ)-\\\dfrac{1}{2}(\cos60^\circ+\cos70^\circ)-\dfrac{1}{2}(\cos50^\circ+\cos60^\circ)=\dfrac{1}{2}\left(-\dfrac{1}{2}+\sin100^\circ-\dfrac{1}{2}-\cos70^\circ-\cos50^\circ-\dfrac{1}{2}\right)=\\\dfrac{1}{2}\left(-\dfrac{3}{2}+\sin100^\circ-\cos70^\circ-\cos50^\circ\right)=-\dfrac{3}{4}+\dfrac{1}{2}(\sin100^\circ-(\cos70^\circ+\cos50^\circ))=\\-\dfrac{3}{4}+\dfrac{1}{2}(\sin100^\circ-2\cos60^\circ\cdot\cos10^\circ)=-\dfrac{3}{4}+\dfrac{1}{2}(\sin(90^\circ+10^\circ)-\cos10^\circ)=\\-\dfrac{3}{4}+\dfrac{1}{2}(\cos10^\circ-\cos10^\circ)=-\dfrac{3}{4}+\dfrac{1}{2}\cdot0=-\dfrac{3}{4}[/tex]

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Žingsnyje [tex]\sin(-30^\circ)=-\sin30^\circ[/tex] taikyta formulė ([tex]\sin(-x)=-\sin x[/tex])
Žingsnyje [tex]\sin(90^\circ+10^\circ)=\cos10^\circ[/tex] taikyta redukcija, nors galima taikyti ir formulę:
[tex]\sin(\alpha+\beta)=\sin\alpha \cos\beta+\cos\alpha \sin\beta[/tex]

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