Question

evaluate: tan5° tan25° tan30° tan65° tan 85°​

Answer 1

Answer:

1/√3

Note :

★ sin(90° - ∅) = cos∅

★ cos(90° - ∅) = sin∅

★ cosec(90° - ∅) = sec∅

★ sec(90° - ∅) = cosec∅

★ tan(90° - ∅) = cot∅

★ cot(90° - ∅) = tan∅

★ tan∅ = sin∅/cos∅

★ cot∅ = cos∅/sin∅

★ cot∅ = 1/tan∅

★ tan∅cot∅ = 1

Solution:

We have ;

=> tan5°•tan25°•tan30°•tan65°•tan 85°

=> tan5°•tan85°•tan30°•tan65°•tan 25°

Also,

• tan85° = cot(90° - 85°) = cot5°

• tan25° = cot(90° - 25°) = cot65°

Thus,

Substituting tan85° = cot5° and

tan25° = cot65° , we get ;

=> tan5°•cot5°•tan30°•tan65°•cot65°

=> 1•tan30°•1

=> tan30°

=> 1/√3

Hence,

Required answer is 1/√3 .