if the pair of equations x + y = root 2 and x sin A + y cos A - Maths - Introduction to Trigonometry

Question

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

Ankush Jain · Accepted Answer

Given equations are, x + y = âˆš2 and x sin A + y cos A = 1 For the given set of equations to have infinitely many solutions, we have $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$ (1) The given equations can be rewritten as: x + y - âˆš2 = 0 x sin A + y cos A - 1 = 0 Using (1), we get $\frac{1}{\sin A} = \frac{1}{\cos A} = \frac{- \sqrt{2}}{- 1}$ â‡’ $\frac{1}{\sin A} = \frac{\sqrt{2}}{1}$ â‡’ $\sin A = \frac{1}{\sqrt{2}}$ â‡’ $\sin A = \sin 45^{\circ}$ â‡’ $A = 45^{\circ}$

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

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