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\( \sqrt{1-\operatorname{Cos} A / 1+\operatorname{Cos} A}+\sqrt{1+\operatorname{Cos} A / 1-\operatorname{Cos} A}= \) |
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Answer» \(\sqrt{\frac{1-cosA}{1+cosA}}+\sqrt{\frac{1+cosA}{1-cosA}}\) = \(\sqrt{\cfrac{1-(1-2sin^2\frac A2)}{1+(2cos^2 \frac A2-1)}}\) + \(\sqrt{\cfrac{1+(2cos^2 \frac A2-1)}{1-(1-2sin^2\frac A2)}}\) = \(\sqrt{\cfrac{2sin^2\frac A2}{2cos^2\frac A2}}\) + \(\sqrt{\cfrac{2cos^2\frac A2}{2sin^2\frac A2}}\) = tan A/2 + cot A/2 |
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