x=2cosa-cos2a,y=2sina-sin2a
To find the values of x and y in terms of a, we can apply trigonometric identities and simplifications. Let's break down each expression step by step:
x = 2cos(a) - cos(2a)
We can use the double-angle formula for cosine, which states that cos(2a) = 2cos^2(a) - 1. Substituting this into the equation:
x = 2cos(a) - 2cos^2(a) + 1
Now, we can combine like-terms:
x = -2cos^2(a) + 2cos(a) + 1
y = 2sin(a) - sin(2a)
Using the double-angle formula for sine, sin(2a) = 2sin(a)cos(a), we can substitute this into the equation:
y = 2sin(a) - 2sin(a)cos(a)
Now that we have simplified forms for x and y, let's recap:
x = -2cos^2(a) + 2cos(a) + 1
y = 2sin(a) - 2sin(a)cos(a)
These equations give the values of x and y in terms of the angle a.