Evaluate :
cot 54°tan 36°\dfrac{\text{cot 54°}}{\text{tan 36°}}tan 36°cot 54° + tan 20°cot 70°\dfrac{\text{tan 20°}}{\text{cot 70°}}cot 70°tan 20° - 2
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cot 54°tan 36°+tan 20°cot 70°−2=cot (90° - 36°)tan 36°+tan (90° - 70°)cot 70°−2=tan 36°tan 36°+cot 70°cot 70°−2=tan36°tan36°+cot70°cot70°−2=1+1−2=2−2=0\dfrac{\text{cot 54°}}{\text{tan 36°}} + \dfrac{\text{tan 20°}}{\text{cot 70°}} - 2\\[1em] = \dfrac{\text{cot (90° - 36°)}}{\text{tan 36°}} + \dfrac{\text{tan (90° - 70°)}}{\text{cot 70°}} - 2\\[1em] = \dfrac{\text{tan 36°}}{\text{tan 36°}} + \dfrac{\text{cot 70°}}{\text{cot 70°}} - 2\\[1em] = \dfrac{\cancel{tan 36°}}{\cancel{tan 36°}} + \dfrac{\cancel{cot 70°}}{\cancel{cot 70°}} - 2\\[1em] = 1 + 1 - 2\\[1em] = 2 - 2\\[1em] = 0tan 36°cot 54°+cot 70°tan 20°−2=tan 36°cot (90° - 36°)+cot 70°tan (90° - 70°)−2=tan 36°tan 36°+cot 70°cot 70°−2=tan36°tan36°+cot70°cot70°−2=1+1−2=2−2=0
Hence, cot 54°tan 36°+tan 20°cot 70°−2=0\dfrac{\text{cot 54°}}{\text{tan 36°}} + \dfrac{\text{tan 20°}}{\text{cot 70°}} - 2 = 0tan 36°cot 54°+cot 70°tan 20°−2=0.
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