Question

Solve it
$\sf \dfrac{cot \theta}{cot \theta - cot3 \theta}+\dfrac{tan\theta}{tan\theta-tan3\theta}$ =

Answer 1

We know that,

Substituting the values,

$\sf \dfrac{cot \theta}{cot \theta - cot3 \theta}+\dfrac{tan\theta}{tan\theta-tan3\theta}$

$\sf = \: 1$

Therefore,

Answer 2

Step-by-step explanation:

Given,

cotθ / cotθ - cot3θ + tanθ / tanθ - tan3θ

To find :-

we have to solve

$\cot(a) \div \cot(a) - \cot(3a)$

Solution:-

$\cot(a) \div \cot(a) - \cot(3a)$

$= > \cot(a) ( \tan(a) - \tan(3a) ) + \tan(a) ( \cot(a) - \cot(3a) ) \div ( \cot(a) - \cot(3a) )( \tan(a) - \tan(3a)$

$= > 1 - \cot(a) \tan(3a) + 1 - \tan(a) \cot(3a) \div 1 - \cot(a) \tan(3a) \\ = > 2 - \cot(a) + \tan(3a) - \tan(a) \cot(3a) \div 2 - \cot(a) \tan(3a) - \tan(a) \cot(3a)$

$hence \: numerators \: and \: denominator \: are \: equal$

So answer is 1