Question #75094
1 Answer
Explanation:
Because
csc(2arctan(3/4))=1/sin(2arctan(3/4))
Using the double angle identity
=1/(2color(blue)(sin(arctan(3/4)))color(red)(cos(arctan(3/4)))
We can find the values of
Note that when
We then see that:
color(blue)(sin(arctan(3/4)))=sin(theta)="opposite"/"hypotenuse"=3/5
color(red)(cos(arctan(3/4)))=cos(theta)="adjacent"/"hypotenuse"=4/5
So the original expression is:
=1/(2color(blue)((3/5))color(red)((4/5)))
=25/24