Question 1198298

given:

{{{sin (x)= 2/7}}}
{{{sin (y)= -1/5}}}
{{{cos(x)= 3sqrt(5)/7}}}
{{{cos (y)= -2sqrt(6)/5}}}


Find 

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

{{{sin(x+y)=( -2sqrt(6)/ 5) (2/7) + (3sqrt(5)/7)(-1/5)}}}

{{{sin(x+y)=-(4sqrt(6))/35-(3sqrt(5))/35}}}

{{{sin(x+y)=-3/(7sqrt(5)) - (4sqrt(6))/35}}}



{{{cos(x+y)=cos(x) cos(y) - sin(x) sin(y)}}}

{{{cos(x+y)=(3sqrt(5)/7) (-2sqrt(6)/ 5) - (2/7) (-1/5)}}}

{{{cos(x+y)=-(6sqrt(30))/35+2/35}}}

{{{cos(x+y)=(2/35) (1 - 3sqrt(30))}}}



{{{ tan(x+y)=sin(x + y)/cos(x + y)}}}

{{{tan(x+y)=(-3/(7sqrt(5)) - (4sqrt(6))/35)/((2/35) (1 - 3sqrt(30)))}}}

{{{tan(x+y)=(1/538) (75sqrt(5) + 49sqrt(6))}}}

{{{tan(x+y)=(1/538) sqrt(3 (14177 + 2450 sqrt(30)))}}}


approximately:

{{{sin(x+y)=-0.4716}}}
{{{cos(x+y)=-0.8818}}}
{{{tan(x+y)=-0.4716/-0.8818=0.53482}}}