Question

It cosec thita = 13/12

find the value of cot thita+tan thita​

Answer 1

Answer:

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Answer 2

Answer:

169/60

Step-by-step explanation:

For simplicity, let's assume angle theta to be equal to angle alpha.

Now, it's given that,

$\csc( \alpha ) = \frac{13}{12}$

To find the value of ,

$\cot( \alpha ) + \tan( \alpha )$

From the question, we have,

$\csc( \alpha ) = \frac{13}{12}$

But, we know that,

• cosec@ = 1/sin@

Therefore, we will get,

$= > \frac{1}{ \sin( \alpha ) } = \frac{13}{12} \\ \\ = > \sin( \alpha ) = \frac{12}{13}$

Now, we know that,

• cos@ = √(1-sin^2@)

Therefore, we will get,

$= > \cos( \alpha ) = \sqrt{1 - {( \frac{12}{13} )}^{2} } \\ \\ = > \cos( \alpha ) = \sqrt{1 - \frac{144}{169} } \\ \\ = > \cos( \alpha ) = \sqrt{ \frac{169 - 144}{169} } \\ \\ = > \cos( \alpha ) = \sqrt{ \frac{25}{169} } \\ \\ = > \cos( \alpha ) = \frac{5}{13}$

Therefore, we will get,

$= > \tan( \alpha ) = \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \\ \\ = > \tan( \alpha ) = \frac{ \frac{12}{13} }{ \frac{5}{13} } \\ \\ = > \tan( \alpha ) = \frac{12}{5}$

Now, we know that,

• cot@ = 1/tan@

Therefore, we will get,

$= > \cot( \alpha ) = \frac{5}{12}$

Therefore, we will get,

$= > \tan( \alpha ) + \cot( \alpha ) = \frac{5}{12} + \frac{12}{5} \\ \\ = > \tan( \alpha ) + \cot( \alpha ) = \frac{25 + 144}{60} \\ \\ = > \tan( \alpha ) + \cot( \alpha ) = \frac{169}{60}$

Hence, the required value id 169/60.