1.

SinA-sin4A/cos4A-cosA=cot5A/2​

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SOLUTION

TO PROVE

\displaystyle \sf{ \frac{ \<klux>SIN</klux> A -  \sin 4A}{\<klux>COS</klux> 4A -  \cos A} =  \cot  \frac{5A}{2}  }

PROOF

\displaystyle \sf{ \frac{ \sin A -  \sin 4A}{\cos 4A -  \cos A} }

\displaystyle \sf{  =  \frac{2\cos \frac{5A}{2}  \: \sin \frac{3A}{2}   }{2\sin \frac{5A}{2}  \: \sin \frac{3A}{2} }  }

\displaystyle \sf{  =  \frac{\cos \frac{5A}{2}    }{\sin \frac{5A}{2}  \: }  }

\displaystyle \sf{  =  \cot \frac{5A}{2}    }

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