geometrically prove that :
1.sin(X-Y) = sinx.cosy-cosx-siny
2. sin(x+y)=sinx.cosy + cosx.siny
3, cos(x+y)= cosx.cosy-sinx.siny
4.tan(x+y)= tanx+tany/1-tanxtany
5. tan(x'y) =tanx-tany/1+tanxtany
Here is the answer for two of the proofs.
Let OX be the initial line.
Let So, Let us choose a point P on OZ.
Draw PM perpendicular to OX and PQ perpendicular to OY. From the point O, draw QN perpendicular to OX and QR perpendicular to PM.
now,
From triangle MOP,
2. sin(x+y)=sinx.cosy + cosx.siny
3, cos(x+y)= cosx.cosy-sinx.siny
Let OX be the initial line.
Let
Draw PM perpendicular to OX and PQ perpendicular to OY. From the point O, draw QN perpendicular to OX and QR perpendicular to PM.
now,
From triangle MOP,