MHT CET · Maths · Application of Derivatives
If \(x+y=\frac{\pi}{2}\), then the maximum value of \(\sin x\).siny is
- A \(\frac{1}{2}\)
- B \(\frac{-1}{2}\)
- C \(\frac{-1}{\sqrt{2}}\)
- D \(\frac{1}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
(C)
\(x+y=\frac{\pi}{2} \quad \Rightarrow \quad y=\frac{\pi}{2}-x\)
\(\sin x \cdot \sin y=\sin x \cdot \sin \left(\frac{\pi}{2}-x\right)=\sin x \cos x=\)\(\frac{2 \sin x \cdot \cos x}{2}=\frac{\sin 2 x}{2} \)
\( \text {We know, }-1 \leq \sin 2 x \leq 1 \Rightarrow \frac{-1}{2} \leq \frac{\sin 2 x}{2} \leq \frac{1}{2}\)
So maximum value is \(\frac{1}{2}\)
\(x+y=\frac{\pi}{2} \quad \Rightarrow \quad y=\frac{\pi}{2}-x\)
\(\sin x \cdot \sin y=\sin x \cdot \sin \left(\frac{\pi}{2}-x\right)=\sin x \cos x=\)\(\frac{2 \sin x \cdot \cos x}{2}=\frac{\sin 2 x}{2} \)
\( \text {We know, }-1 \leq \sin 2 x \leq 1 \Rightarrow \frac{-1}{2} \leq \frac{\sin 2 x}{2} \leq \frac{1}{2}\)
So maximum value is \(\frac{1}{2}\)
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
- The principal solutions of \(\cot x+\sqrt{3}=0\) areMHT CET 2022 Easy
- The principal solutions of \(\cos 2 x=\frac{-1}{2}\) areMHT CET 2020 Easy
- In a triangle \(\mathrm{ABC}\), with usual notations, if \(\mathrm{c}=4\), then value of \((a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}\) isMHT CET 2023 Hard
- If , then at isMHT CET 2018 Easy
- A particle is moving on a straight line. The distance \(\mathrm{S}\) travelled in time \(t\) is given by \(S=a t^2+b t+6\). If the particle comes to rest after 4 seconds at a distance of \(16 \mathrm{~m}\). from the starting point, then the acceleration of the particle is.MHT CET 2021 Easy
- The standard deviation of the following distribution is
MHT CET 2023 Easy
More PYQs from MHT CET
- The time period of a simple pendulum inside a stationary lift is \(\sqrt{3}\) second. When the lift moves upwards with an acceleration \(\mathrm{g} / 3\), the time period will be ( \(\mathrm{g}=\) acceleration due to gravity)MHT CET 2025 Medium
- Guttation occurs through __________ .MHT CET 2014 Hard
- Freundlich adsorption isotherm isMHT CET 2007 Hard
- Which of the following solutions will have highest boiling point?MHT CET 2008 Medium
- The molar conductivities at infinite dilution for sodium acetate, HCI and NaCI are 91 S and respectively. The molar conductivity of acetic acid at infinite dilution isMHT CET 2019 Hard
- Which of the following solutions on complete dissociation exhibits maximum elevation in boiling point?MHT CET 2024 Easy