Question

Să se aducă la o formă mai simplă expresia cos(a+b)+sin a • sin b/cos(a-b)-sin a• sin b

Answer 1

   
[tex]\displaystyle\\ \bf\\ \text{folosim formulele:}\\ \cos (a+b) = \cos a \cdot \cos b - \sin a \cdot \sin b \\ \cos (a-b) = \cos a \cdot \cos b + \sin a \cdot \sin b \\\\ \text{Rezolvare:}\\\\\\ \frac{\cos(a+b)+\sin a \cdot \sin b}{cos(a-b)-\sin a\cdot \sin b} =\\\\\\ =\frac{ \cos a \cdot \cos b \overbrace{- \sin a \cdot \sin b+\sin a \cdot \sin b}^{=0}}{\cos a \cdot \cos b + \underbrace{\sin a \cdot \sin b-\sin a\cdot \sin b}_{=0}} = \frac{ \cos a \cdot \cos b}{ \cos a \cdot \cos b}=\boxed{1}[/tex]