Question

if
sinx+sin y=1/4, cos X+ cosy=1/3 then tan (x+y/2)=​

Answer 1

Answer:

cosx+cosy=1/3……………equation1

sinx+siny=1/4………..equation2

Squaring both the sides of equation 1&2

Cos2x+cos2y+2cosx×cosy=1/9

sin2x+sin2y+2sinx×siny=1/16

After squaring add new equations

Cos and sin terms will add and will be equal to one.

Sin2x+cos2x=1

sin2y+cos2y=1

2(1+cosxcosy+sinxsiny)=25/144

Cosxcosy+sinxsiny=(25/288)−1

cos(x−y)=−263/288