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If cos a= -23/27, find cos a/6?

If cos a= -23/27, find cos a/6?

Grade:

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:Hello student, please find answer to your question
cos(6x) = 4cos^{3}(2x)-3cos(2x)
cos(a) = 4cos^{3}(\frac{a}{3})-3cos(\frac{a}{3})
\frac{-23}{27} = 4cos^{3}(\frac{a}{3})-3cos(\frac{a}{3})
108cos^{3}(\frac{a}{3})-81cos(\frac{a}{3}) + 23 = 0
\frac{a}{3} = 2\pi n\pm cos^{-1}(\frac{-1-2\sqrt{6}}{6}), 2\pi n\pm cos^{-1}(\frac{2\sqrt{6}-1}{6})
\frac{a}{6} = \frac{2\pi n\pm cos^{-1}(\frac{-1-2\sqrt{6}}{6})}{2}, \frac{2\pi n\pm cos^{-1}(\frac{2\sqrt{6}-1}{6})}{2}

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