Question

Sin x + y =1/3 and cos x + cos y=1/4 then cot(x+y/2) =

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Answer 1

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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} )