Question

$tan5^{0}\times tan30^{0}\times4tan85^{0}$ is equal to
(a)4/√3
(b)4√3
(c)1
(d)4

Answer 1

SOLUTION :  

The correct option is (a) : 4/√3

We have to find the value of : tan 5° × tan 30° × 4 tan 85°  

tan 5° × tan 30° × 4 tan 85°  

= tan (90° - 85°) × tan 30° × 4 tan 85°  

= cot 85° ×  tan 30° × 4 tan 85°  

[ tan (90° - θ) = cot θ]

= cot 85° ×  tan 30° × 4 tan 85°  

= 4(cot 85° × tan 85°) ×  tan 30°

= 4 × 1 × 1/√3

[ cot θ × tan θ = 1,  tan 30° = 1/√3]

= 4/√3

tan 5° × tan 30° × 4 tan 85° = 4/√3  

Hence, the value of tan 5° × tan 30° × 4 tan 85° is 4/√3 .

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

Answer:

Option(A)

Step-by-step explanation:

Given Equation is tan5° * tan30° * 4tan85°

∴ tan θ = (1/cot θ)

= tan(90-85) * tan30 * 4(1/cot85)

∴ tan(90 - θ) = cot θ.

= cot85 * (1/√3) * (4/cot85)

= (4/√3).

Hope it helps!