Respuesta :
Answer:
cos2x = - [tex]\frac{7}{25}[/tex]
Step-by-step explanation:
Given
sinx = [tex]\frac{4}{5}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
This is a right triangle with sides 3- 4- 5
cosx < 0 , thus
cosx = [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{3}{5}[/tex]
Using the trig. identity
cos2x = cos²x - sin²x , then
cos2x = (- [tex]\frac{3}{5}[/tex] )² - ( [tex]\frac{4}{5}[/tex] )² = [tex]\frac{9}{25}[/tex] - [tex]\frac{16}{25}[/tex] = - [tex]\frac{7}{25}[/tex]
