The value of frac{{3 + cot ,7,{6^ circ },cot | vedclass

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Question

Using $\frac{{3\,\sin {{76}^0}\,.\,\sin {{16}^0}\, + \,\cos {{76}^0}\,\cos {{16}^0}}}{{\cos {{76}^0}\,\sin {{16}^0}\, + \,\sin {{76}^0}\,\cos {{1

Vedclass · Accepted Answer

$cot \,44^&ordm;$

Vedclass · Answer

Using $\frac{{3\,\sin {{76}^0}\,.\,\sin {{16}^0}\, + \,\cos {{76}^0}\,\cos {{16}^0}}}{{\cos {{76}^0}\,\sin {{16}^0}\, + \,\sin {{76}^0}\,\cos {{16}^0}}}$

$=$ $\frac{{2\,\sin {{76}^0}\,\sin {{16}^0}\, + \,[\sin {{76}^0}\,\sin {{16}^0}\, + \,\cos {{76}^0}\,\cos {{16}^0}]}}{{\sin {{92}^0}}}$ 

$=$ $\frac{{\cos 60^\circ  - \cos 92^\circ  + \cos 60^\circ }}{{\sin 92^\circ }}$

$=$$\frac{{1 - \cos {{92}^0}}}{{\sin {{92}^0}}}$ $=$$\frac{{2\,{{\sin }^2}{{46}^0}}}{{2\,\sin {{46}^0}\,\cos {{46}^0}}}\,$ $= tan 46^o = cot44^o$

The value of $\frac{{3 + \cot \,7\,{6^ \circ }\,\cot \,{{16}^ \circ }}}{{\cot \,{{76}^ \circ } + \cot \,{{16}^ \circ }}}$ is :

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