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