Question

If cosx+cosy=1/3 and sinx+siny =1/4 then tan(x+y)/2 =

Answer 1

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Answer 2

Answer:

$\frac{3}{4}$

Step-by-step explanation:

We have given,

cosx + cosy = 1/3,

$\implies 2\cos(\frac{x+y}{2}).\cos (\frac{x-y}{2})=\frac{1}{3}----(1)$

sinx + siny = 1/4,

$\implies 2\sin (\frac{x+y}{2}).\cos (\frac{x-y}{2})=\frac{1}{4}----(2)$

Dividing equation (2)  by (1),

We get,

$\frac{\sin (\frac{x+y}{2})}{\cos (\frac{x+y}{2})}=\frac{1/4}{1/3}=\frac{3}{4}$

$\implies \tan (\frac{x+y}{2})=\frac{3}{4}$

( $\because \tan x=\frac{\sin x}{\cos x}$ )