Question

find cot 10 cot 50 cot 70

Answer 1

Answer:

trick of this question is

1/3tan3x=1/4tan10×3=1×√3/4

Answer 2

The correct answer is $\sqrt{3}$.

Given: The equation = cot10°cot50°cot70°.

To Find: The value of equation.

Solution:

As we know the identity.

tanxtan(60-x) tan(60+x) = tan3x

Do the reciprocal both the sides.

$\frac{1}{tanxtan(60-x) tan(60+x)} = \frac{1}{tan3x}$

cotxcot(60-x)cot(60+x) = cot3x

Put x = 10 in this equation.

cot10°cot(60°-10°)cot(60°+10°)

cot10°cot50°cot70°

= cot3(10°)

= cot 30°

= $\sqrt{3}$

Hence, the correct answer is $\sqrt{3 }$.

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