Question

Show that tan 7
°
X tan 23°X tan 60°X tan 67°X tan 83° = √3​

Answer 1

evaluate,

tan7
∘
tan23
∘
tan60
∘
tan67
∘
tan83
∘


We know that,
tan(90−θ)=cotθ and cotθ=
tanθ
1
​


tan7
∘
=tan(90
∘
−83
∘
)=cot83
∘

tan23
∘
=tan(90
∘
−67
∘
)=cot67
∘


∴tan7
∘
tan23
∘
tan60
∘
tan67
∘
tan83
∘


=cot83
∘
cot67
∘
tan60
∘
tan67
∘
tan83
∘


=
tan83
∘

1
​

tan67
∘

1
​
tan60
∘
tan67
∘
tan83
∘


=
tan83
∘
tan67
∘

tan60
∘
tan67
∘
tan83
∘

​


=tan60
∘


=underroot 3