Question

cos 7A +Cos 5A/sin7A -sin5A=​

Answer 1

$\begin{gathered}\Large{\bold{{\underline{Formula \: Used - }}}}  \end{gathered}$

$\boxed{{\bf \: sinx - siny = 2cos\bigg( \dfrac{x + y}{2} \bigg)sin\bigg( \dfrac{x - y}{2} \bigg)}}$

$\boxed{{\bf \: cosx + cosy = 2cos\bigg( \dfrac{x + y}{2} \bigg)cos\bigg( \dfrac{x - y}{2} \bigg)}}$

$\large\underline{\bf{Solution-}}$

$\rm :\longmapsto\:\dfrac{cos7A + cos5A}{sin7A - sin5A}$

$\sf \: \: \: \: = \: \: \dfrac{ \cancel2cos\bigg( \dfrac{7A + 5A}{2} \bigg)cos\bigg( \dfrac{7A - 5A}{2} \bigg)}{ \cancel2cos\bigg( \dfrac{7A + 5A}{2} \bigg)sin\bigg( \dfrac{7A - 5A}{2} \bigg)}$

$\sf \: \: \: \: = \: \: \dfrac{ \cancel{cos6A} \: cosA}{ \cancel{cos6A} \: sinA}$

$\sf \: \: \: \: = \: \: cotA$

Additional Information :-

$\boxed{{\bf \: sinx + siny = 2sin\bigg( \dfrac{x + y}{2} \bigg)cos\bigg( \dfrac{x - y}{2} \bigg)}}$

$\boxed{{\bf \: cosx - cosy = 2sin\bigg( \dfrac{x + y}{2} \bigg)sin\bigg( \dfrac{y - x}{2} \bigg)}}$

$\boxed{{\bf \: 2sinxcosy = sin(x + y) + sin(x - y)}}$

$\boxed{{\bf \: 2cosxcosy = cos(x + y) + cos(x - y)}}$

$\boxed{{\bf \: 2sinxsiny = cos(x - y) - cos(x + y)}}$