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If 2*cos(x) + 3*sin(x) = sqrt(13), what are cos(x) and sin(x)?

 Jan 4, 2021
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I can tell you that $cos(x) + sin(x) = \frac{5}{\sqrt{13}},$ so $2 \cdot cos(x) + 2\cdot sin(x) = \frac{10}{\sqrt{13}}.$ Subtracting, $sin(x) = \frac{3\sqrt{13}}{13}.$ Can you find $cos(x)$ now?

 Jan 4, 2021

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