[tex]\sin\theta=\dfrac45\implies\cos\theta=\dfrac35[/tex]
[tex]\sin\varphi=\dfrac5{13}\implies\cos\varphi=\dfrac{12}{13}[/tex]
[tex]\tan\theta=\dfrac{\sin\theta}{\cos\theta}=\dfrac45[/tex]
[tex]\tan\varphi=\dfrac{\sin\varphi}{\cos\varphi}=\dfrac5{12}[/tex]
[tex]\tan(\theta+\varphi)=\dfrac{\tan\theta+\tan\varphi}{1-\tan\theta\tan\varphi}=\dfrac{63}{16}[/tex]
