Respuesta :

[tex]\sin\left(2\cos^{-1}\dfrac7{25}\right)=2\sin\left(\cos^{-1}\dfrac7{25}\right)\cos\left(\cos^{-1}\dfrac7{25}\right)[/tex]
[tex]=2\dfrac{24}{25}\dfrac7{25}[/tex]
[tex]=\dfrac{336}{625}[/tex]

Answer:

0.5377

Step-by-step explanation:

the correct expression can be written as

[tex]sin(2 cos^{-1}\frac{7}{25})[/tex]

[tex]cos^{-1}\frac{7}{25}[/tex]= 73.739°

now sin(2\times73.739)= sin(147.47)

= 0.5377

therefore the exact value of the expression

[tex]sin(2 cos^{-1}\frac{7}{25})[/tex]= 0.5377

please pay attention on each step, hope this helps.