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| 1. |
Prove that {1-tanA ÷ 1-cotA } = tan^2A |
| Answer» {tex}\\begin{array}{l}\\left(\\frac{1-\\mathrm{tanA}}{1-\\mathrm{cotA}}\\right)^2=\\left(\\frac{1-\\mathrm{tanA}}{1-{\\displaystyle\\frac1{\\mathrm{tanA}}}}\\right)^2\\\\=\\left(\\mathrm{tanA}\\frac{(1-\\mathrm{tanA})}{\\mathrm{tanA}-1}\\right)^2\\\\=(-\\mathrm{tanA})^2=\\tan^2\\mathrm A\\end{array}{/tex} | |