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 =

Question

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 =, 4, 1, 2, 0

MARKS App · Accepted Answer

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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