Question

The equation $3 \cos x + 4 \sin x = 6$ has

• A. Finite solution
• B. Infinite solution
• C. One solution
• D. No solution

Answer 1

Answer: (D)

No solution

Answer 2

$3 \cos x + 4 \sin x = 6$

$\Rightarrow$ $\frac { 3 } { 5 } \cos x + \frac { 4 } { 5 } \sin x = \frac { 6 } { 5 }$ $\Rightarrow$ $\cos ( x - \theta ) = \frac { 6 } { 5 }$ $\left[ \therefore \theta = \cos ^ { - 1 } \left( \frac { 3 } { 5 } \right) \right]$

So that equation has no solution.