if the pair of equations x + y = root 2. and x sin A + y cos A = 1 has infinitely many solutions, then A = ?

options : 30, 45, 60 and 90

**Given** equations are,

*x* + *y* = √2 and

*x *sin A + *y *cos A = 1

For the given set of equations to have infinitely many solutions, we have

... (1)

The given equations can be rewritten as:

*x* + *y* - √2 = 0

*x *sin A + *y *cos A - 1 = 0

Using (1), we get

⇒

⇒

⇒

⇒

**
**