sin 300° × cot 210° × sec 315° =
[tex]\fcolorbox{violet}{violet}{✧ bismillahirrahmanirrahim ✧}[/tex]
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[tex] = - \frac{3 \sqrt{2} }{2} \\ [/tex]
[tex] \\ [/tex]
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[tex] \sin(300°) \times \cot(210°) \times \sec(315°) = \\ [/tex]
[tex] = - \frac{ \sqrt{3} }{2} \times \cot(210°) \times \sec(315°) \\ [/tex]
[tex] = - \frac{ \sqrt{3} }{2} \times \sqrt{3} \times \sec(315°) \\ [/tex]
[tex] = - \frac{ \sqrt{3} }{2} \times \sqrt{3} \times \sqrt{2} \\ [/tex]
[tex] = - \frac{ \sqrt{3 \times 3 \times 3} }{2} \\ [/tex]
[tex] = - \frac{ \sqrt{18} }{2} \\ [/tex]
[tex] = \sqrt{ {3}^{2} } \sqrt{2} \\ [/tex]
[tex] = - \frac{3 \sqrt{2} }{2} \\ [/tex]
[tex] \\ [/tex]
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[tex]\fcolorbox{violet}{violet}{ -- Answer By @blqzzz01 || Brainly -- }[/tex]
❐ Trigonometri
[tex] \rm \to -\dfrac {3\sqrt{2}}{2} [/tex]
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Pembahasan
[tex] \rm = sin~300° \times cot~210° \times sec~315° [/tex]
[tex] \rm = sin~(360°-60°) \times cot~(180°+30°) \times sec~(360°-45°) [/tex]
[tex] \rm = -sin~60° \times \dfrac {-cos~30°}{-sin~30°} \times \dfrac {1}{cos~45°} [/tex]
[tex] \rm = -\dfrac {1}{2}\sqrt{3} \times \dfrac {-\frac{1}{2}\sqrt{3}}{-\frac{1}{2}} \times \dfrac {1}{\frac {1}{2}\sqrt{2}} [/tex]
[tex] \rm = -\dfrac {1}{2}\sqrt{3} \times \sqrt{3} \times \sqrt {2} [/tex]
[tex] \rm = -\dfrac{1}{2}\sqrt{18} [/tex]
[tex] \rm = -\dfrac {3\sqrt{2}}{2} [/tex]
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