Question

Find the value of cot10° × cot20° × cot60° × cot70° × cot 80°

Answer 1

Hey sup!

As per the question,

cot10° × cot20° × cot60° × cot70° × cot 80°.

=cot(90°-80°)×cot(90°-70°)×cot60°×cot70°×cot80°. {Cot(90°-A)=tanA)

=tan80°×tan70°×cot60°×cot70°×cot80°.

=tan80°×cot80°×tan70°×cot70°×cot60°.

=1×1×cot60°. {tanA×cotA=1)}.

=cot60°.

=1/√3.

Hope it helps.

Answer 2

The value of cot10° × cot20° × cot60° × cot70° × cot 80° =$\dfrac{1}{\sqrt{3}}$.

Step-by-step explanation:

We have,

cot10° × cot20° × cot60° × cot70° × cot 80°

To find, the value of  cot10° × cot20° × cot60° × cot70° × cot 80° = ?

∴ cot10° × cot20° × cot60° × cot70° × cot 80°

=  cot10° × cot20° × cot60° × cot(90° - 20°) × cot (90° - 10°)

= cot10° × cot20° × cot60° × tan20° × tan 10°

[ ∵ cot(90° - A) = tan A]

= (cot10°× tan 10°) × (cot20°× tan20° ) × cot60°

= (1) × (1) × cot60°

[ ∵ cotA × tan A = 1]

= cot60°

= $\dfrac{1}{\sqrt{3}}$

Hence, the value of cot10° × cot20° × cot60° × cot70° × cot 80° = $\dfrac{1}{\sqrt{3}}$.