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If sinx +siny=a and cosx +cosy=b then find sin(x+y)and cos(x+y)
If sinx +siny=a and cosx +cosy=b then find sin(x+y)and cos(x+y)

```
3 years ago

```							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)
```
3 years ago
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