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Solve for x cosx + (3) 1/2 sinx = 2cos2x I would really appreciate if you reply soon.

Solve for x
cosx + (3)1/2sinx = 2cos2x
I would really appreciate if you reply soon.

Grade:11

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:Hello student, please find answer to your question
cosx + \sqrt{3}sinx = 2cos2x
\frac{1}{2}.cosx + \frac{\sqrt{3}}{2}sinx = \frac{2}{2}.cos2x
cos(a+b) = cosa.cosb - sina.sinb
cos(x - \frac{\pi }{3})= cos2x
2x = 2n\pi \pm (x - \frac{\pi }{3})
2x\mp x = 2n\pi \mp \frac{\pi }{3}
x = 2n\pi \mp \frac{\pi }{3}, \frac{1}{3}.(2n\pi \mp \frac{\pi }{3})

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