1.

cos(x+y)=cosx cosy-sinx siny

Answer»

Let x+y= c, a constant

Let A(x)=cos(x)cos(c-x)-sin(x)sin(c-x)=cos(x)cos(y)-sin(x)sin(y)

If we know the differentiations of sin(x) and of cos(x), then it can be shown that A’(x)=0

Let if x=0, Then A(0)= 1*cos(c)= 0*sin(c)=cos(c)= cos(x+y)= constant,

so, A(x)=cos(x+y)=cos*x)cos(y)=sin(x)sin(y)


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