Question

if sin x =k sin (x +y) show that tan(x+y)=sin y/cos y-k

Answer 1

Answer:

sin(x-y)=sin(x)cos(y)- cos(x)sin(y)

And

sin(x+y)=sin(x)cos(y)+cos(x)sin(y)

Thus,

sin(x)cos(y)- cos(x)sin(y)=k[sin(x)cos(y)+cos(x)sin(y)]

Divide both LHS and RHS by cos(x)cos(y) and you get:

[sin(x)cos(y)- cos(x)sin(y)]/cos(x)cos(y)=k[sin(x)cos(y)+cos(x)sin(y)]/cos(x)cos(y)

tan(x)-tan(y)=k[tan(x)+tan(y)]

(1-k)tan(x)=(1+k)tan(y)

tan(x)=[(1+k)/(1-k)]tan(y)

Answer 2

Answer:

here is your answer..................................