Question

1 The value of
tan 30°
cot 60°
is
1​

Answer 1

Answer:

the value of cot60° an tan 30° is 1/√3

Answer 2

Answer:

Hence Proved !

Step-by-step explanation:

Tan and cot are trigonometric ratios. They work only in a right angle triangle.

• Tan is found out by dividing the opposite side by the adjacent side.

$\tan\theta = \frac{opposite \: side}{adjacent \: side}$

• Cot is found out by dividing the adjacent side by the opposite side.

$\cot\theta = \frac{adjacent \: side}{opposite \: side}$

We can clearly see that the product of tan and cot = 1, as cot is the reciprocal of tan.

i.e. $\: \tan\theta \times \cot \theta = 1.$

But here we are directly provided with the value of θ

$\\ \\ In \: \tan\theta : \theta = 30^{\circ} \\ \\ In \cot \theta : \theta = 60^{\circ}$

$\frac{ \tan30^{\circ} }{ \cot60^{\circ} } = \frac{ \frac{1}{ \sqrt{3} } }{ \frac{1}{ \sqrt{3} } }$

The values of tan 30° and cot 60° are constant and can't be changed.

$\frac{ \frac{1}{ \sqrt{3} } }{ \frac{1}{ \sqrt{3} } } = \frac{1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{1} = 1$

√3 and √3 get cancelled.

So,

$\: \frac{ \tan30^{\circ} }{ \cot60^{\circ} } = 1.$