Question

without using trigonometric tables prove that tan 5°tan 25°tan30°tan65°tan85°=1/✓3​

Answer 1

Answer:

Tan 5 = tan(90-85) = cot85

Tan 25 = Tan(90-65) = Cot65

Tan5 Tan25 Tan30 Tan 65 Tan85

⇒ Cot85 Cot 65 Tan30 Tan65 Tan85

⇒ Tan 30 (Since Cot85*Tan85 = 1 and Cot65*Tan65 = 1)

⇒ 1/_/3

Answer 2

Step-by-step explanation:

tan5°.tan25°.tan30°.tan65°.tan85°=(1/√3)

tan5°.tan85°.tan25°.tan65°.tan30°=(1/√3)

tan5°.cot(90°-85°).tan25°.cot(90°-25°).tan30°=

(1/√3)

tan5°.cot5°.tan25°.cot25°.tan30°=(1/√3)

(tan5°/tan5°).(tan25°/tan25°).(1/√3)=(1/√3)

(1).(1).(1/√3)=(1/√3)

(1/√3)=(1/√3)

LHS = RHS

Hence proved