cosx+cosy=a and sinx+siny=b show that sin2x+sin2y=2ab(1-(2/(a^2+b^2))

Question

plz plz show step

Answer 1

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!

Answer 2

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

Answer 3

I am Leo I Just changed my name to Steve because I thought I'd get in trouble

Answer 4

If you can help a student, why would you get into trouble?

Nice work, by the way.

Answer 5

how did
sin(x+y)=2sinxsiny
is it not suppose to be
sin(2x)

Answer 6

It is very easy and amazing

Answer 7

Thank u for your solution