cosx+cosy=a and sinx+siny=b show that sin2x+sin2y=2ab(1-(2/(a^2+b^2))
plz plz show step
how did
sin(x+y)=2sinxsiny
is it not suppose to be
sin(2x)
Thank u for your solution
Let A = (X+Y)/2 and B = (X-Y)/2.
a = sin X + sin Y = sin(A+B) + sin(A-B) = 2 sin A cos B
b = cos X + cos Y = cos(A+B) + cos(A-B) = 2 cos A cos B
a/b = (2 sin A cos B) / (2 cos A cos B) = tan A
sin A = a/√(a² + b²)
cos A = b/√(a² + b²)
sin(X+Y) = sin 2A = 2 sin A cos A = 2ab / (a² + b²)
cos(2X + 2Y) = cos 4A = 1 - 2 sin² 2A
cos(2X + 2Y) = 1 - 4a²b² / (a² + b²)²
cos(2X + 2Y) = (a² - b²)² / (a² + b²)²
I am Leo I Just changed my name to Steve because I thought I'd get in trouble
If you can help a student, why would you get into trouble?
Nice work, by the way.
It is very easy and amazing
x = arccos (a - cos(y))
y = arccos (a/2)
a = cos (x) + cos(y)
I have no idea but those above are what they equal but I am sure someone else can provide you help. Good Luck!