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The value of tan ⁡ 63 o - cot ⁡ 63 o is equal to

Options

  1. A2 5 + 1 10 - 2 5
  2. B2 5 + 1 10 + 2 5
  3. C5 - 1 4 10 - 2 5
  4. D5 - 1 4 10 + 2 5

Correct answer

A. 2 5 + 1 10 - 2 5

Step-by-step solution

sin ⁡ 63 o cos ⁡ 63 o - cos ⁡ 63 o sin ⁡ 63 o = s i n 2 63 o - cos 2 ⁡ 63 o cos ⁡ 63 o sin ⁡ 63 o = - cos ⁡ 126 o 1 2 sin ⁡ 126 o = - 2 cot ⁡ 126 o = - 2 c o t π 2 + 3 6 ∘ = 2 t a n 3 6 ∘ = 2 s i n 3 6 ∘ c o s 3 6 ∘ = 2 5 + 1 10 - 2 5

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