Step-by-step explanation:
[tex]\sin\dfrac{40}{41}\cos\dfrac{24}{25}+\cos\dfrac{40}{41}\sin\dfrac{24}{25}\\\\\text{Use}\ \sin(x+y)=\sin x\cos y+\sin y\cos x\\\\=\sin\left(\dfrac{40}{41}+\dfrac{24}{25}\right)=\sin\left(\dfrac{(40)(25)}{(41)(25)}+\dfrac{(41)(24)}{(41)(25)}\right)\\\\=\sin\left(\dfrac{1000+984}{1025}\right)=\sin\dfrac{1984}{1025}\approx0.9342[/tex]
