\(cosx + cosy = 2cos\dfrac{x + y}{2} cos\dfrac{x - y}{2}\)
\(cosx - cosy = -2sin\dfrac{x + y}{2}sin\dfrac{x - y}{2}\)
\(sinx + siny = 2sin\dfrac{x + y}{2} cos\dfrac{x - y}{2}\)
\(sinx - siny = 2cos\dfrac{x + y}{2} sin\dfrac{x - y}{2}\)
\(tanx + tany = \dfrac{sin (x + y) }{cosx.cosy}\)
\(tanx - tany = \dfrac{sin (x - y) }{cosx.cosy}\)
\(cotx + coty = \dfrac{sin (x + y) }{sinx.siny}\)
\(cotx - coty = \dfrac{sin (y - x) }{sinx.siny}\)
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