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AP EAMCET202023 Sep 2020Morning ShiftMathematicsTrigonometric Ratios & IdentitiesActual

If cos θ 1 + cos θ 2 + cos θ 3 + cos θ 4 = - 4 , then the value of cot θ 1 2 + cot θ 2 2 + cot θ 3 2 + cot θ 4 2 =

Options

  1. A4
  2. B1
  3. C2
  4. D0

Correct answer

D. 0

Step-by-step solution

Given, cos ( θ 1 ) +   cos ( θ 2 ) + cos ( θ 3 ) +   cos ( θ 4 ) = - 4 We know that, 1 ≤ cos ( θ ) ≤ 1 cos ( θ 1 ) = - 1 , cos ( θ 2 ) = - 1 , cos ( θ 3 ) = - 1 , cos ( θ 4 ) = - 1 θ 1 = π =   θ 2 =   θ 3 =   θ 4 ⇒ cot π 2 + cot π 2 + cot π 2 + cot π 2 ⇒ 4 cot π 2 ⇒ 0   ∵ cot π 2 = 0

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