AP EAMCET · Maths · Inverse Trigonometric Functions
If \(0 \lt x \lt \frac{1}{2}\) and \(\alpha=\sin ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{\sqrt{3-3 x^2}}{2}\right)\), then \(\tan \alpha+\cot \alpha=\)
- A \(\frac{4}{\sqrt{3}}\)
- B \(4 \sqrt{3}\)
- C \(\frac{4 x}{1-x^2}\)
- D \(x \sqrt{1-x^2}\)
Answer & Solution
Correct Answer
(A) \(\frac{4}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Given that \(\begin{aligned} & \alpha=\sin ^{-1} x+\cos ^{-1}\left(\frac{x}{2}+\frac{\sqrt{3-3 x^2}}{2}\right), 0 \lt x \lt \frac{1}{2} \\ & \Rightarrow \alpha=\sin ^{-1} x+\cos ^{-1}\left(\frac{1}{2} \cdot x+\frac{\sqrt{3}}{2} \cdot \sqrt{1-x^2}\right) \end{aligned}\) Let…
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
- If in a \(\triangle A B C, \frac{1}{a+c}+\frac{1}{b+c}=\frac{3}{a+b+c}\), then \(\angle C\) is equal toAP EAMCET 2013 Medium
- If a circle with radius 2.5 units passes through the points \((2,3)\) and \((5,7)\), then its centre isAP EAMCET 2017 Medium
- If the position vectors of the vertices \(A, B, C\) of a triangle are \(3 \bar{i}+4 \bar{j}-\bar{k}\), \(\overline{\mathrm{i}}+3 \overline{\mathrm{j}}+\overline{\mathrm{k}}, 5(\overline{\mathrm{i}}+\overline{\mathrm{j}}+\overline{\mathrm{k}})\) respectively, then the magnitude of the altitude drawn from \(A\) on to the side \(B C\) isAP EAMCET 2025 Medium
- If there is an error of \(\pm 0.04 \mathrm{~cm}\) in the measurement of the diameter of a sphere, then the approximate percentage error in its volume, when the radius is \(10 \mathrm{~cm}\), isAP EAMCET 2014 Hard
- If \(f(x)=\int \operatorname{cosec}^5 x d x\), then \(f\left(\frac{\pi}{4}\right)=\)AP EAMCET 2018 Medium
- The solution of \(x \frac{d y}{d x}=y(\log y-\log x+1)\) isAP EAMCET 2020 Easy
More PYQs from AP EAMCET
- In how many of the following compounds of sulphur, the oxidation state of sulphur atom isAP EAMCET 2019 Medium
- Two identical bodies have temperatures \(277^{\circ} \mathrm{C}\) and \(67^{\circ} \mathrm{C}\). If the surroundings temperature is \(27^{\circ} \mathrm{C}\), the ratio of loss of heats of the two bodies during the same interval of time is (approximately)AP EAMCET 2005 Easy
- For which value of ' \(k\) ', the roots of equation \(2 x^2+5 x+k=0\) are rational?AP EAMCET 2020 Medium
- \(\int \frac{e^x-1}{e^x+1} d x=\)AP EAMCET 2017 Medium
- \(160 \mathrm{~g}\) of non-volatile solute ' \(A\) ' is dissolved in \(54 \mathrm{~mL}\) of water at \(373 \mathrm{~K}\). What is the vapour pressure of aqueous solution of \(A\). (Given, molecular weight of \(A=160 \mathrm{~g} \mathrm{~mol}^{-1}\) )AP EAMCET 2020 Medium
- The correct formula used to determine the formal charge \(\left(\mathrm{Q}_{\mathrm{f}}\right)\) on an atom in the given Lewis structure of a molecule or ion is
( \(\mathrm{V}=\) number of valence electrons in free atom, \(\mathrm{U}=\) number of unshared electrons on the atom, \(\mathrm{B}=\) number of bonds around the atom)AP EAMCET 2024 Easy