Question

if the pair of linear equations x+y=√2 and xsinA+ycosA=1 has infinitely many solutions, then what is the value of A.​

Answer 1

Answer:

the answer is 45°

Step-by-step explanation:

If the pair of equations x sin theta + y cos theta = |

and x + y = √2 has infinitely many solutions then the value of theta = 45°

Answer 2

Given:

A pair of linear equations x+y=√2 and xsinA + ycosA = 1 has infinitely many solutions.

To find:

The value of A.

Solution:

A pair of linear equations ax + by = c and mx + ny = d is said to have infinitely many solutions if

$\frac{a}{m} = \frac{b}{n} = \frac{c}{d}$

So, on comparing the above with a pair of linear equations x+y=√2 and xsinA + ycosA = 1 that is given in the question, we have

a = 1, b = 1, c = √2, m = sinA, n = cosA and d = 1.

Thus, using the above formula for infinitely many solutions, we have,

$\frac{1}{sinA} = \frac{1}{cosA} = \frac{√2}{1}$

$\frac{1}{sinA} = \frac{√2}{1} \: and \: \frac{1}{cosA} = \frac{√2}{1}$

$sinA = cosA = \frac{1}{√2}$ (i)

Using trigonometric ratios, we have

$sin45° = cos45° = \frac{1}{√2}$ (ii)

On comparing (i) and (ii), we have,

A = 45°

Hence, the value of A is 45°.