Answer:
25*√((2-√3)/2)
Step-by-step explanation:
Use the identity: cos(x)=sin(90°-x)
cos(75°)=sin(90°-75°)=25sin(90°-75°)
Simplify
25sin(15°)
then write sin(15°) as sin(30°/2)
Use the half-angle identity: sin(x/2)= ((1-cos(x))/2)^(1/2)
((1-cos(30°))/2)^(1/2) cos(30°)=((3)^(1/2))/2
then plug that in for the cos(30°) and solve
√((2-√3)/2) multiply by 25
25*√((2-√3)/2)
