Question

tan 5° ✕ tan 30° ✕ 4 tan 85° is equal to 

पर्याय

• `4/sqrt3`

• `4sqrt3`

• 1

• 4

Answer 1

We have to find `tan 5°xx tan 30° xx4 tan 85°` 

We know that 

`tan (90°-θ)=cot-θ` 

`tan  θ cot -θ=1` 

`tan 30°=1/sqrt3` 

so 

`tan 5° xx tan 30° xx 4 tan 85°` 

=` tan (90°-85°)xx tan 30°xx4 tan 85°` 

= `cot 85° xx tan 30°xx4 tan 85°` 

=` 4 cot 85° xx tan 85° tan 30°` 

= `4xx1xx1/sqrt3`  

= `4/sqrt3`