\operatorname { tan } 5 \operatorname { tan } 25 ^ { \circ } \operator

1.	\operatorname { tan } 5 \operatorname { tan } 25 ^ { \circ } \operatorname { tan } 30 ^ { \circ } \operatorname { tan } 65 ^ { \circ } \operatorname { tan } 85 ^ { \circ } = \frac { 1 } { \sqrt { 3 } }
Answer» Tan 5 = tan(90-85) = cot85Tan 25 = Tan(90-65) = Cot65 Tan5 Tan25 Tan30 Tan 65 Tan85⇒ Cot85 Cot 65 Tan30 Tan65 Tan85⇒ Tan 30 = 1/√3 (Since Cot85Tan85 = 1 and Cot65Tan65 = 1)

\operatorname { tan } 5 \operatorname { tan } 25 ^ { \circ } \operatorname { tan } 30 ^ { \circ } \operatorname { tan } 65 ^ { \circ } \operatorname { tan } 85 ^ { \circ } = \frac { 1 } { \sqrt { 3 } }

Answer»

Tan 5 = tan(90-85) = cot85Tan 25 = Tan(90-65) = Cot65

Tan5 Tan25 Tan30 Tan 65 Tan85⇒ Cot85 Cot 65 Tan30 Tan65 Tan85⇒ Tan 30 = 1/√3

(Since Cot85*Tan85 = 1 and Cot65*Tan65 = 1)