If tan⁡(π12−x),tan⁡π12,tan⁡(π12+x)\tan\left(\frac{\pi}{12} - x\right), \tan\frac{\pi}{12}, \tan\left(\frac{\pi}{12} + x\right)…

Mathematics

Problem

If tan⁡(π12−x),tan⁡π12,tan⁡(π12+x)\tan\left(\frac{\pi}{12} - x\right), \tan\frac{\pi}{12}, \tan\left(\frac{\pi}{12} + x\right) in order are three consecutive terms of a G.P. then sum of all the solutions in [0,314][0, 314] is kπk\pi. The value of kk is : (a) 4950 (b) 5050 (c) 2525 (d) 5010

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