TS EAMCET · Maths · Inverse Trigonometric Functions
\(\sin \mathrm{h}^{-1}\left(2^{3 / 2}\right)\) is equal to :
- A \(\log (3+\sqrt{8})\)
- B \(\log (3-\sqrt{8})\)
- C \(\log (2+\sqrt{18})\)
- D \(\log (\sqrt{8}+\sqrt{27})\)
Answer & Solution
Correct Answer
(A) \(\log (3+\sqrt{8})\)
Step-by-step Solution
Detailed explanation
We have \(\sin h^{-1} x=\log \left\{x+\sqrt{x^2+1}\right\}\) \(\sin h^{-1}(2)^{3 / 2}=\log \left\{2^{3 / 2}+\sqrt{\left(2^{3 / 2}\right)^2+1}\right\}\) \(=\log \{\sqrt{8}+\sqrt{8+1}\}=\log \{3+\sqrt{8}\}\)
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 number of common tangents that can be drawn to the circles and isTS EAMCET 2021 Medium
- Urn A contains 6 white and 2 black balls; urn B contains 5 white and 3 black balls and urn C contains 4 white and 4 black balls. If an urn is chosen at random and a ball is drawn at random from it, then the probability that the ball drawn is white isTS EAMCET 2025 Medium
- 10 men and 6 women are to be seated in a row so that no two women sit together. The number of ways they can be seated, isTS EAMCET 2013 Easy
- All the letters of the word 'COLLEGE' are arranged in all possible ways and all the seven letter words (with or without meaning) thus formed are arranged in the dictionary order. Then the rank of the word 'COLLEGE' isTS EAMCET 2024 Easy
- Consider the following statements.
a) If a function is differentiable at a point then it is not continuous at
b) If a function is not continuous at then it is not differentiable at
c) If then is not differentiable but continuous on
d) If then
Which of the above statements are (is) correct?TS EAMCET 2021 Easy - \(x\) and \(y\) are two positive integers such that \(2 x+3 y=50\). If \(x^2 y^3\) is maximum for \(x=\alpha\) and \(y=\beta\), then \(\frac{\alpha}{2}+\frac{\beta}{5}=\)TS EAMCET 2023 Easy
More PYQs from TS EAMCET
- If the radical axis of the circles \(x^2+y^2+2 \alpha x+2 \beta y+c=0\) and \(x^2+y^2+\frac{3}{2} x+4 y+c=0\) touches the circle \(x^2+y^2+2 x+2 y+1=0\), then \(4 \alpha \beta-8 \alpha-3 \beta+10=\)TS EAMCET 2020 Hard
- Identify the logic gate for which the output is when any of the inputs isTS EAMCET 2021 Easy
- Which one of the following ions has same number of unpaired electrons as those present in \(\mathrm{V}^{3+}\) ion?TS EAMCET 2014 Easy
- Which of the following statements regarding the first law of thermodynamics is correct?TS EAMCET 2020 Easy
- Consider the curves and Assertion : The common tangents to the curves and are orthogonal. Reason : and are the common tangents to the curves andTS EAMCET 2019 Medium
- The equation of the circle that touches the -axis at a distance of units from the origin and cuts off an intercept of units on the -axis isTS EAMCET 2019 Easy