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If π 2 < α < 3 π 4 , then 2 tan ⁡ α + 1 c o s 2 α is equal to

Options

  1. A- 1 + tan ⁡ α
  2. B- 1 - tan ⁡ α
  3. C1 + tan ⁡ α
  4. D1 - tan ⁡ α

Correct answer

B. - 1 - tan ⁡ α

Step-by-step solution

2 tan ⁡ α + 1 c o s 2 α = 2 tan ⁡ α + s e c 2 α = 2 tan ⁡ α + 1 + t a n 2 α = 1 + tan ⁡ α 2 = 1 + tan ⁡ α Since, tan ⁡ α < - 1 when π 2 < α < 3 π 4 ⇒ 1 + tan ⁡ α < 0 ⇒ 1 + tan ⁡ α = - 1 - tan ⁡ α

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