MHT CET · Maths · Inverse Trigonometric Functions
The value of \(\sin \left(\cos ^{-1}\left(-\frac{1}{3}\right)-\sin ^{-1}\left(\frac{1}{3}\right)\right)\) is
- A 1
- B 3
- C 2
- D 4
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \sin \left(\cos ^{-1}\left(-\frac{1}{3}\right)-\sin ^{-1}\left(\frac{1}{3}\right)\right) \\ & =\sin \left(\cos ^{-1}\left(-\frac{1}{3}\right)-\left[\frac{\pi}{2}-\cos ^{-1}\left(\frac{1}{3}\right)\right]\right) \\ & =\sin \left(\left[\pi-\cos ^{-1}\left(\frac{1}{3}\right)\right]-\frac{\pi}{2}+\cos ^{-1}\left(\frac{1}{3}\right)\right) \\ & =\sin \left(\frac{\pi}{2}\right) \\ & =1\end{aligned}\)
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
- \(\int_0^1|5 x-3| d x=\)MHT CET 2021 Medium
- The symbolic form of the following circuit is (where and \(s_{2}\) closed respectively)
MHT CET 2020 Hard - \(\int_{0}^{1} \tan ^{-1}\left[\frac{2 x-1}{1+x-x^{2}}\right] d x=\)MHT CET 2020 Hard
- The equation of a curve whose normal at any point has a slope which is the same as the ordinate and which passes through \((1,-1)\) is \(2 x=\mathrm{k}\left(3-\mathrm{y}^2\right)\). Then k isMHT CET 2025 Medium
- The general solution of the differential equation \(\frac{d y}{d x}=\frac{3 x+y}{x-y}\) is (where \(C\) is a constant of integration.)MHT CET 2022 Medium
- \(\mathrm{A}\) and \(\mathrm{B}\) are independent events with \(\mathrm{P}(\mathrm{A})=\frac{1}{4}\) and \(P(A \cup B)=2 P(B)-P(A)\), then \(P(B)\) isMHT CET 2023 Easy
More PYQs from MHT CET
- A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability, that a student will get 4 or more correct answers just by guessing, isMHT CET 2024 Easy
- Which ligand among the following has highest splitting power of d-orbitals of central metal ion?MHT CET 2020 Easy
- With an increase in temperature, surface tension of liquid (except molten copper and cadmium)MHT CET 2010 Medium
- If \(P(2,2), Q(-2,4)\) and \(R(3,4)\) are the vertices of \(\triangle P Q R\), then the equation of the median through vertex, \(R\) is \(\_\_\_\_\)MHT CET 2019 Easy
- A mass attached to a spring performs S.H.M. whose displacement is \(\mathrm{x}=3 \times 10^{-3} \cos 2 \pi \mathrm{t}\) metre. The time taken to obtain maximum speed for the first time isMHT CET 2025 Medium
- A metal sphere cools at a rate of \(1.5^{\circ} \mathrm{C} / \mathrm{min}\) when its temperature is \(80^{\circ} \mathrm{C}\). When the temperature of the sphere is \(40^{\circ} \mathrm{C}\), its rate of cooling is \(0.3^{\circ} \mathrm{C} / \mathrm{min}\). The temperature of the surrounding \(\left(\theta_0\right)\) isMHT CET 2025 Medium