Question

Find the value of tan30°/cot60°

Answer 1

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.

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

$But \: here, \: we \: are \: directly \\ provided \: with \: the \: value \: of \: \theta . \\ \\ In \: \tan\theta : \theta = 30^{\circ} \\ \\ In \cot \theta : \theta = 60^{\circ}$

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

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.

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

Answer 2

given :- tan30°/cot60°

we know that :-

→ tan30° = 1/√3

→ cot60° = 1/√3

therefore tan30°/cot60° = 1/√3 * √3/1

= √3/√3

= 1

hence, the value of tan30°/cot60° is 1.

HOPE THIS HELPS..!!