Question

If tan x = k tan y, show that ( k-1 )sin (x+y)=(k+1) sin (x-y)

Give answer only those who know! ​

Answer 1

Answer:

1

Step-by-step explanation:

tan x / tan y = k

(sinx/cosx)/(siny/cosy)=k

sixcosy/coxsiny=k

sinxcosy=kcosxsiny---(1)

LHS:

(k-1)sin(x+y)=(k-1)(sinxcosy+cosxsiny)=ksinxcosy+kcosxsiny-sinxcosy-cosxsiny

=ksinxcosy+sinxcosy-sinxcosy-cosxsiny[from(1)]

=ksinxcosy-cosxsiny

RHS:

(k+1)(sinxcosy-cosxsiny)

=ksinxcosy-kcosxsiny+sinxcosy-cosxsiny

=ksinxcosy-sinxcosy+sinxcosy-cosxsiny[from (1)]

=ksinxcosy-cosxsiny=LHS

so

LHS=RHS