# If cos(x-y) =12/13, sin(x+y) =3/5 , then tan 2y is equal to

Solution:

$\\ cos(x-y)=12/13\\ \\\Rightarrow tan(x-y)=5/12\\ \\\Rightarrow sin(x+y)=3/5\Rightarrow tan(x+y)=3/4$

Now, $\\ 2y=[(x+y)-(x-y)]$

Take tan both side we get

$\\tan 2y=tan[(x+y)-(x-y)]= tan(x+y)-tan(x-y)/1+tan(x+y)\times tan(x-y)\\ \\\Rightarrow tan2y=(3/4-5/12)/(1+3/4\times 5/12)=16/63$

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