Question

Prove that,Cos3x+Cos7x-Cos2x/Sin7x-Sin3x-Sin2x=Cot2x

Answer 1

hope this helps you☺️

Answer 2

 To prove:          $\frac{Cos3x+Cos7x-Cos2x}{Sin7x-Sin3x-Sin2x} =Cot2x$

LHS:             $\frac{(Cos7x+Cos3x)-Cos2x}{(Sin7x-Sin3x)-Sin2x}$

   ⇒     $\frac{2Cos\frac{3x+7x}{2}Cos\frac{7x-3x}{2}-Cos2x }{2Cos\frac{7x+3x}{2}Sin\frac{7x-3x}{2} -Sin2x }$

   ⇒      $\frac{2Cos5xCos2x-Cos2x}{2Cos5xSin2x-Sin2x}$

   ⇒      $\frac{Cos2x(2Cos5x-1}{Sin2x(2Cos5x-1)}$

   ⇒       $\frac{Cos2x}{Sin2x}$

   ⇒      $Cot2x$

RHS:     $Cot2x$

$LHS=RHS$

hence proved....

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