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Question

cot5tan52tan104tan208tan40 is
  1. 0
  2. 4tan40
  3. 8tan40
  4. 8cot40


Solution

The correct option is A 0
cotθtanθ= cosθsinθsinθcosθ= cos2θsin2θsinθcosθ= 2cos2θsin2θ=2cot2θcotθtanθ=2cot2θ

So, cot5tan5 = 2cot10
So, 2cot102tan10 = 4cot20
So, 4cot204tan20 = 8cot40
Adding the three equations we get, cot5tan52tan104tan208tan40 = 0

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