Question

Допоможіть....... терміново

Answer 1

$\displaystyle\bf\\\alpha \ i \ \beta \in\Big(0 \ ; \ \frac{\pi }{2}\Big) \ \ \Rightarrow \ \ Cos\alpha > 0 \ \ , \ \ Cos\beta > 0\\\\\\Sin\alpha =\frac{1}{\sqrt{5} } \ \ \ , \ \ \ Sin\beta =\frac{\sqrt{15} }{4} \\\\\\Cos(\alpha + \beta)\cdot Cos\alpha+Sin(\alpha + \beta )\cdot Sin\alpha =Cos(\alpha + \beta - \alpha)=Cos\beta \\\\\\Cos\beta =\sqrt{1-Sin^{2}\beta }=\sqrt{1-\Big(\frac{\sqrt{15} }{4} \Big)^{2} } =\sqrt{1-\frac{15}{16} }=\sqrt{\frac{1}{16} }=\frac{1}{4}$