The-value-of-cot16-cot44-cot44-cot76-cot76-cot16-is-

Question Number 18742 by Tinkutara last updated on 31/Jul/17

The value of \cot 16 ° \cot 44 ° + \cot 44 ° \cot 76 °

- \cot 76 ° \cot 16 ° is

Answered by Tinkutara last updated on 31/Jul/17

\frac{3 + \cot 76 ° \cot 16 °}{\cot 76 ° + \cot 16 °}

= \frac{3 \sin 76 ° \sin 16 ° + \cos 76 ° \cos 16 °}{\sin (76 ° + 16 °)}

= \frac{2 \sin 76 ° \sin 16 ° + \cos (76 ° - 16 °)}{\sin 92 °}

= \frac{\cos 60 ° - \cos 92 ° + \cos 60 °}{\sin 92 °}

= \frac{1 - \cos 92 °}{\sin 92 °} = \tan 46 ° = \cot 44 °

Now, \frac{3 + \cot 76 ° \cot 16 °}{\cot 76 ° + \cot 16 °} = \cot 44 °

\cot 16 ° \cot 44 ° + \cot 44 ° \cot 76 ° - \cot 76 ° \cot 16 ° = 3