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[tex] \cos( \frac{7\pi}{12} ) = [/tex]
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Răspuns :

[tex]\bf cos\bigg(\dfrac{7\pi }{12} \bigg)= cos \bigg(\dfrac{4\pi +3\pi }{12} \bigg) =\\\bf cos\bigg(\dfrac{3\pi }{12}^{(3} + \dfrac{4\pi }{12}^{(4} \bigg) = cos \bigg( \dfrac{\pi }{4} + \dfrac{\pi }{3} \bigg) =\\\bf cos \bigg(\dfrac{\pi }{4} \bigg) \cdot cos \bigg(\dfrac{\pi }{3} \bigg) - sin \bigg( \dfrac{\pi }{4} \bigg) \cdot sin\bigg(\dfrac{\pi }{3} \bigg) =\\\bf =\dfrac{\sqrt{2} }{2} \cdot \dfrac{1}{2} -\dfrac{\sqrt{2} }{2} \cdot \dfrac{\sqrt{3} }{2} =\dfrac{\sqrt{2} }{4} - \dfrac{\sqrt{6} }{4} \bf \iff[/tex]

[tex]\bf \iff \boxed{\bf \dfrac{\sqrt{2}-\sqrt{6} }{4} }[/tex]

[tex]\bf \;[/tex]

[tex]\;[/tex][tex]\bf sin(\, 30^{\circ} ) = \dfrac{1}{2}[/tex]

[tex]\bf sin(\, 45^{\circ})=\dfrac{\sqrt{2} }{2}[/tex]

[tex]\bf sin (\, 60^{\circ}) = \dfrac{\sqrt{3} }{2}[/tex]

[tex]\bf \;[/tex]

[tex]\bf cos(\, 30^{\circ})=\dfrac{\sqrt{3} }{2}[/tex]

[tex]\bf cos(\, 45^{\circ})=\dfrac{\sqrt{2} }{2}[/tex]

[tex]\bf cos(\, 60^{\circ})=\dfrac{1}{2}[/tex]

cos ( 7π / 12 ) = ?

= cos ( π / 4 + π / 3 )

= cos ( π / 4) cos ( π / 3 ) - sin ( π / 4 ) sin ( π / 3 )

= √2/2  * 1/2 - √2/2 - √3/2

= √2/2 * 1/2 - √2/2 * √3/2

= ( √2 - √6 ) / 4