KCET · Maths · Trigonometric Equations
The number of solutions for the equation \(\sin 2 x+\cos 4 x=2\) is
- A 0
- B 1
- C 2
- D \(\infty\)
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
Given, \(\sin 2 x+\cos 4 x=2\)
\[
\begin{array}{ll}
\Rightarrow & \sin 2 x+1-2 \sin ^{2} 2 x=2 \\
\Rightarrow & 2 \sin ^{2} 2 x-\sin 2 x+1=0
\end{array}
\]
Now, Discriminant, \(\mathrm{D}=(-1)^{2}-4 \cdot 2 \cdot 1=-7 < 0\)
Hence, it is an imaginary equation, so the real roots does not exist.
\[
\begin{array}{ll}
\Rightarrow & \sin 2 x+1-2 \sin ^{2} 2 x=2 \\
\Rightarrow & 2 \sin ^{2} 2 x-\sin 2 x+1=0
\end{array}
\]
Now, Discriminant, \(\mathrm{D}=(-1)^{2}-4 \cdot 2 \cdot 1=-7 < 0\)
Hence, it is an imaginary equation, so the real roots does not exist.
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