KCET · Maths · Trigonometric Equations
If \(\sin 2 x=4 \cos x\), then \(x\) is equal to
- A \(\frac{\mathrm{n} \pi}{2} \pm \frac{\pi}{4}, \mathrm{n} \in \mathrm{Z}\)
- B no value
- C \(n \pi+(-1)^{n} \frac{\pi}{4}, n \in Z\)
- D \(2 \mathrm{n} \pi \pm \frac{\pi}{2}, \mathrm{n} \in \mathrm{Z}\)
Answer & Solution
Correct Answer
(D) \(2 \mathrm{n} \pi \pm \frac{\pi}{2}, \mathrm{n} \in \mathrm{Z}\)
Step-by-step Solution
Detailed explanation
Given, \(\sin 2 x=4 \cos x\)
\[
\begin{aligned}
&\Rightarrow \quad 2 \sin x \cos x=4 \cos x \\
&\Rightarrow \quad 2 \cos x(\sin x-2)=0
\end{aligned}
\]
\(\Rightarrow \sin x=2\), which is not possible because the value of \(\sin x\) lies between \(-1\) and 1 .
\(\therefore \quad \cos \mathrm{x}=0\)
\(\Rightarrow \quad x=2 n \pi \pm \frac{\pi}{2}\)
\[
\begin{aligned}
&\Rightarrow \quad 2 \sin x \cos x=4 \cos x \\
&\Rightarrow \quad 2 \cos x(\sin x-2)=0
\end{aligned}
\]
\(\Rightarrow \sin x=2\), which is not possible because the value of \(\sin x\) lies between \(-1\) and 1 .
\(\therefore \quad \cos \mathrm{x}=0\)
\(\Rightarrow \quad x=2 n \pi \pm \frac{\pi}{2}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(a, b, c, d\) and \(e\) be the observations with mean \(m\) and standard deviation \(S\). The standard deviation of the observations \(a+k\), \(b+k, c+k, d+k\) and \(e+k\) isKCET 2024 Easy
- The maximum value of \( \left(\frac{1}{x}\right)^{x} \) isKCET 2018 Hard
- If \(A=\left[\begin{array}{rr}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\), then \(A \cdot A^{\prime}\) isKCET 2011 Easy
- The equation of the normal to the curve \( y\left(1+x^{2}\right)=2-x \) where the tangent crosses \( x \)-axis isKCET 2016 Medium
- The contrapositive of the converse of the statement "If \( x \) is a prime number then \( x \) is odd" isKCET 2016 Medium
- If \(3 x+i(4 x-y)=6-i\) where \(x\) and \(y\) are real numbers, then the values of \(x\) and \(y\) are respectively,KCET 2022 Easy
More PYQs from KCET
- Mercury is a liquid metal becauseKCET 2008 Easy
- The codon on mRNA are CAU-CCU-AAA-CUG. Identify the correct sequence of amino acids.KCET 2018 Medium
- With regard to the ABO blood typing system, if a man who has type B blood and a woman who has type O blood were to have children, what blood types could be children have?KCET 2012 Medium
- The value of \(\cot ^{-1}\left[\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}\right]\), where \(x \in\left(0, \frac{\pi}{4}\right)\) isKCET 2023 Hard
- A man weighs \(80\) kg. He stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of \(6 \text{ m/s}^2\). What would be his weight in kg? (\(g = 10 \text{ m/s}^2\))KCET 2026 Medium
- Two capillary tubes \(P\) and \(Q\) are dipped vertically in water. The height of water level in capillary tube \(P\) is \(\frac{2}{3}\) of the height in capillary tube \(Q\). The ratio of their diameter isKCET 2021 Medium