Question

The number of solutions for the equation $Sin\, 2x + Cos \; 4x = 2$ is

• A. $0$
• B. $1$
• C. $2$
• D. $\infty$

Answer 1

Answer: (A)

$0$

Answer 2

Given, $\sin 2 x+\cos 4 x=2$
$\Rightarrow \,\,\,\,\sin 2 x+1-2 \sin ^{2} 2 x=2$
$\Rightarrow \,\,\,\,\,2 \sin ^{2} 2 x-\sin 2 x+1=0$
Now, Discriminant, $D=(-1)^{2}-4 \times 2 \times 1=-7 < 0$
Hence, it is an imaginary equation, so the real roots does not exist.