Answer:
Therefore [tex]\cos(\alpha-\beta)=\frac{48+7\sqrt{25}}{125}[/tex]
Step-by-step explanation:
Given values are
[tex]\sin \alpha=\frac{7}{25}[/tex]
[tex]\cos \beta=\frac{2}{5}[/tex]
[tex]\sin^2x+\cos^2=1[/tex]
[tex]\cos \alpha=\sqrt{1-\sin^2\alpha}[/tex]
[tex]\cos \alpha=\sqrt{1-(\frac{7}{25})^2}[/tex]
[tex]\cos \alpha=\sqrt{1-\frac{49}{625}}[/tex]
[tex]\cos \alpha=\sqrt{\frac{576}{625}}[/tex]
[tex]\cos \alpha=\frac{24}{25}[/tex]
[tex]\sin \beta=\sqrt{1-\cos^2\beta}[/tex]
[tex]\sin \beta=\sqrt{1-(\frac{2}{5})^2}[/tex]
[tex]\sin \beta=\sqrt{1-\frac{4}{25}}[/tex]
[tex]\sin \beta=\frac{\sqrt{21}}{5}[/tex]
[tex]\cos(\alpha-\beta)=\cos\alpha\cos\beta+\sin\alpha\sin\beta[/tex]
[tex]\cos(\alpha-\beta)=\frac{24}{25}\times\frac{2}{5}+\frac{7}{25}\times\frac{\sqrt{21}}{5}[/tex]
[tex]\cos(\alpha-\beta)=\frac{48+7\sqrt{25}}{125}[/tex]
