Question

Tan 5 × tan 30 ×4 tan 85 is equal to

Answer 1

tan 5 × tan 30 × 4 tan 85 

tan 5 × tan 30 × 4 × tan 85 

tan ( 90 - 85) × tan 30 × 4 x tan 85 

cot 85 × tan 30 × 4 x tan 85

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We know, 

tan 30 = 1/√3 

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cot 85 × 1/√3 × 4 x tan85 

1/tan85 x 1/√3 x 4 x tan85

1 x 4 × 1/√3 

4/√3

4*√3/√3*√3

4√3/3

Answer 2

Answer:4/√3 or 4√3/3

Step-by-step explanation:

Tan 5° × Tan 30° × 4Tan 85°

Tan (90°-85°) × Tan 30° × 4Tan 85°

Cot 85° × Tan 30° × 4Tan 85°. (Tan(90°- a) = Cot a

4 × 1/√3. (Tan 30°=1/√3, Cot a×Tan a =1)

4/√3

If we rationalise denominator it will be like this

4/√3× √3/√3

4√3/3

That's all

This is answer