The value of $$cot$$⁡$$36$$∘$$cot$$⁡$$72$$∘ is

Question

The value of $$cot$$⁡$$36$$∘$$cot$$⁡$$72$$∘ is

Infinity Learn · Accepted Answer

We find $$thatcot2$$⁡$$36$$∘$$cot2$$⁡$$72$$∘$$=cos2$$⁡$$36$$∘$$cos2$$⁡$$72$$∘$$sin2$$⁡$$36$$∘$$sin2$$⁡$$72$$∘$$=1+$$$$cos$$⁡$$72$$∘$$1+$$$$cos$$⁡$$144$$∘$$1$$−$$cos$$⁡$$72$$∘$$1$$−$$cos$$⁡$$144$$∘$$=1+$$$$cos$$⁡$$72$$∘$$1$$−$$cos$$⁡$$36$$∘$$1$$−$$cos$$⁡$$72$$∘$$1+$$$$cos$$⁡$$36$$∘$$=1+$$$$cos$$⁡$$72$$∘−$$cos$$⁡$$36$$∘−$$cos$$⁡$$72$$∘$$cos$$⁡$$36$$∘$$1$$−$$cos$$⁡$$72$$∘$$+$$$$cos$$⁡$$36$$∘−$$cos$$⁡$$72$$∘$$cos$$⁡$$36$$∘$$=1$$−$$cos$$⁡$$36$$∘−$$cos$$⁡$$72$$∘−$$cos$$⁡$$72$$∘$$cos$$⁡$$36$$∘$$1+$$$$cos$$⁡$$36$$∘−$$cos$$⁡$$72$$∘−$$cos$$⁡$$72$$∘$$cos$$⁡$$36$$∘$$=1$$−$$12$$−$$141+12$$−$$14=15$$             ∵$$cos$$⁡$$36$$∘−$$cos$$⁡$$72$$∘$$=12$$ and, $$cos$$⁡$$36$$∘$$cos$$⁡$$72$$∘$$=14$$∴ $$cot2$$⁡$$36$$∘$$cot2$$⁡$$72$$∘$$=15$$⇒$$cot$$⁡$$36$$∘$$cot$$⁡$$72$$∘$$=15$$

The value of $\cot 36^{\circ} \cot 72^{\circ}$ is

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The value of cot⁡36∘cot⁡72∘ is

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The value of $\cot 36^{\circ} \cot 72^{\circ}$ is