Question

cos(x-y)=3 cos(x+y) then prove that cotx city =2​

Answer 1

Answer is in attachment

thank you

Answer 2

Answer:

The required proof of $cotxcoty=2$ is shown in the explanation section.

Step-by-step explanation:

Given : $cos(x-y)= 3\times cos(x+y)$

To prove: $cotx\times coty = 2$

Proof:

$cos(x-y)= 3\times cos(x+y)$

$cosxcosy+sinxsiny =3(cosxcosy-sinxsiny)$

Rearranging similar terms in LHS and RHS,

$2cosxcosy= 4 sinxsiny$

Dividing throughout by $sinxsiny$ we get,

$\frac{cosxcoty}{sinxsiny} =\frac{4}{2}$

∴

$cotxcoty=2$

Hence, the required is proved.