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If sinx +siny=a and cosx +cosy=b then find sin(x+y)and cos(x+y)
sinx + siny = a 2sin(x+y/2)cos(x-y/2) = a ......................1 (by using sum formula) cosx + cosy = b 2cos(x-y/2)cos(x+y/2) = b ..................2 divide both tan(x+y/2) = a/b ...........3 tan2@ = sec2@ - 1 & sec@ = 1/cos@ so cos(x+y/2) = [b2/a2+b2]1/2 ......................4 sin(x+y/2) = {1-cos2(x+y/2)}1/2 = [a2/a2+b2]1/2.............5 sinx+y = 2sin(x+y/2)cos(x+y/2) (sinA = 2sinA/2cosA/2) from eq 4 & 5 sin(x+y )= 2ab/a2+b2 similarily we can deduce cos (x +y)
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