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The value of 3+cot⁡76∘cot⁡16∘cot⁡76∘+cot⁡16∘  is

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a
cot 44°
b
cot 46°
c
tan 2∞
d
cot 92∞

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detailed solution

Correct option is A

We can write 4+cot⁡76∘cot⁡16∘−1cot⁡76∘+cot⁡16∘=4sin⁡76∘sin⁡16∘sin⁡92∘+cot⁡92∘=2cos⁡60∘−cos⁡92∘+cos⁡92∘sin⁡92∘=1−cos⁡92∘sin⁡92∘=cot⁡46∘=tan⁡44∘

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