The solution set of the system of equations x - y - 2 -3- cos x -cos y -3-2- where x and y are real- is

We have cosx + cosy =3/2 or 2 cos ( x+y/2 )cos ( x y/2 )=3/2 or 2 cos π/3cos ( x y/2 )=3/2 [ising:x +y =2π/3] or cos ( x y/2 )=3/2, which is not possible. H ...

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Standard XIII

Mathematics

Solving Simultaneous Trigonometric Equations

The solution ...

Question

The solution set of the system of equations $x + y = \frac{2 π}{3}, c o s x + c o s y = \frac{3}{2}$ , where x and y are real, is ___

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Solution

We have $c o s x + c o s y = \frac{3}{2}$
or $2 c o s (\frac{x + y}{2}) c o s (\frac{x - y}{2}) = \frac{3}{2}$
or $2 c o s \frac{π}{3} c o s (\frac{x - y}{2}) = \frac{3}{2} [i s i n g : x + y = \frac{2 π}{3}]$
or $c o s (\frac{x - y}{2}) = \frac{3}{2}$ , which is not possible.
Hence, the system of equations has no solution.

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The solution set of the system of equations x+y=2π3,cosx+cosy=32, where x and y are real, is ___

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