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  • Value of  <img alt="\frac{3+ \cot 80 \degree \cos 20\degree}{\cot 80\degree + \cot 20\degree }" src="https://learn.careers360.com/latex-image/?%5Cfrac%7B3&plus;%20%5Ccot%2080%20%5Cdegree%2

Value of  \frac{3+ \cot 80 \degree \cos 20\degree}{\cot 80\degree + \cot 20\degree } is equal to

Option: 1

\cot 20\degree


Option: 2

\tan 50 \degree


Option: 3

\cot 50 \degree


Option: 4

\cot \degree \sqrt {20 }


Answers (1)

best_answer

As we have learnt in

 

Addition Formulae -

\sin \left ( A+B \right )= \sin A\cos B+\cos A\sin B

- wherein

A and B are two angles.

 

 

Subtraction Formulae -

\cos \left ( A-B \right )= \cos A\cos B+\sin A\sin B

- wherein

A and B are two angles.

 

 

Transformation Formulae -

- wherein

These formula are also called A-B formulae.

 

 

\frac{3+ \frac{\cos 80 \degree \cos 20\degree}{\sin 80\degree \sin 20\degree}}{\frac{\cos 80\degree }{\sin 80\degree } +\frac{\cos 20\degree }{\sin 20\degree }}\\\\ 

= \frac{2 \sin 80 \degree\sin 20\degree + \cos 80\degree \cos 20\degree + \sin 80\degree \sin 20\degree }{\sin 20\degree \cos 80\degree + \cos 20\degree \sin 80 \degree} \\\\ \frac{\cos 60\degree - \cos 100\degree + \cos 60 \degree}{\sin 100\degree } = \frac{1- \cos 100 \degree}{\sin 100\degree } \\\\= \tan 50 \degree

Posted by

Ajit Kumar Dubey

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