sina+sinb=0 cosa+cosb=0 find cos2a+cos2b

 the ans is 0.

expand cos2a as cos²a - sin²a

then gropu similar terms

you get the asnwer aas zero!!

cos2a+cos2b=2cos((2a+2b)/2)cos((2a-2b)/2)=2cos(a+b).cos(a-b)=2Cos²a-cos²b=2(cosa+cosb)(cosa-cosb)=0

squaring and adding...
2+2(cos a-b)=0
cos a-b = -1
again,
squaring and subtracting,
cos 2a + cos 2b + 2cos a+b =0
cos 2a + cos 2b = -2cos a+b
but cos a-b = -1
hence a and b differ by angle pi
so a=np/2..b=3npi/2
hecne a+b=2npi...cos a+b=1
so cos2a + cos 2b=1 ANS.