Question

Prove that tan 5 degree Tan 25 degree tan 30 degree tan 65 degree tan 85 degree = 1 by root 3​

Answer 1

Answer: tan 5°× tan 25° ×tan 30° ×tan 65°× tan 85°

= tan 5°× tan 85° ×tan 65° ×tan 25°× tan 30°

using the identity given below

= cot (90° - 5°) ×tan 85°× cot(90° - 65°)× tan 25°× tan 30°

= cot 85°× tan 85°× cot 25°× tan 25°× tan 30°

now we use identity no. 2 given below

finally we get,

= tan 30° = 1 / √3

Step-by-step explanation: as we know about complementary angles

from the identity

tan ∅ = cot(90° - ∅) or vice versa

and identity no.2

tan ∅× cot∅ = 1