In a triangle A B C , if sin ⁡ A cos ⁡ B = 1 4 and 3 tan ⁡ A = tan ⁡ B , then cot 2 ⁡ A is equal to

Question

In a triangle A B C , if sin ⁡ A cos ⁡ B = 1 4 and 3 tan ⁡ A = tan ⁡ B , then cot 2 ⁡ A is equal to, 2, 3, 4, 5

MARKS App · Accepted Answer

3 sin ⁡ A cos ⁡ B = sin ⁡ B cos ⁡ A ⇒ cos ⁡ A sin ⁡ B = 3 4 ⇒ sin ⁡ A + B = 1 ⇒ C = π 2 , B = π 2 - A 3 tan ⁡ A = tan ⁡ π 2 - A = cot ⁡ A ⇒ cot 2 ⁡ A = 3

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