TS EAMCET · Maths · Inverse Trigonometric Functions
If \(\tan ^{-1} \frac{1}{5}+\frac{1}{2} \sec ^{-1} x+\tan ^{-1} \frac{1}{8}=\frac{\pi}{8}\), then \(x^2=\)
- A \(\frac{12}{7}\)
- B \(\frac{50}{49}\)
- C \(\frac{13}{12}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{50}{49}\)
Step-by-step Solution
Detailed explanation
We have, \(\begin{array}{r} \tan ^{-1} \frac{1}{5}+\frac{1}{2} \sec ^{-1} x+\tan ^{-1} \frac{1}{8}=\frac{\pi}{8} \\ \Rightarrow \quad\left(\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{8}\right)+\frac{1}{2} \sec ^{-1} x=\frac{\pi}{8} \end{array}\)…
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 the perpendicular distance from the focus of an ellipse \(\frac{x^2}{9}+\frac{y^2}{b^2}=1(b < 3)\) to its corresponding directrix is \(\frac{4}{\sqrt{5}}\), then the slope of the tangent to this ellipse drawn at \(\left(\frac{3}{\sqrt{2}}, \frac{b}{\sqrt{2}}\right)\) isTS EAMCET 2025 Medium
- The angle between the lines \(\hat{\mathbf{r}}=(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}})+\lambda(\hat{\mathbf{i}}+4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \quad\) and \(\hat{\mathbf{r}}=(\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}})+\mu(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})\) isTS EAMCET 2014 Medium
- If two dice are thrown, then the probability of getting coprime numbers on the dice isTS EAMCET 2024 Easy
- If \(f(x)=10 \cos x+(13+2 x) \sin x, \quad\) then \(f^{\prime \prime}(x)+f(x)\) is equal toTS EAMCET 2005 Hard
- If \(\tan A\) and \(\tan B\) are the roots of the quadratic equation \(x^2-p x+q=0\), then \(\sin ^2(A+B)\) is equal toTS EAMCET 2011 Medium
- The height of a right circular cylinder is decreasing while is diameter is increasing at a rate of \(4 \mathrm{~cm} / \mathrm{see}\) so as to keep its volume unchanged. the rate of change in its lateral surface area (in \(\mathrm{cm}^2 / \mathrm{sec}\) ) at the instant when its diameter is \(8 \mathrm{~cm}\) and height is \(12 \mathrm{~cm}\), isTS EAMCET 2019 Hard
More PYQs from TS EAMCET
- A long straight solenoid with a cross-sectional radius and number of turns per unit length has a current varying with time as The magnitude of the electric field as a function of distance from the solenoid axis is,TS EAMCET 2021 Easy
- If \(\frac{x^4}{(x-1)(x-2)(x-3)}=p(x)+\frac{A}{x-1}+\frac{B}{x-2}+\frac{C}{x-3}\) then \(p\left(\frac{3}{2}\right)+\mathrm{C}=\)TS EAMCET 2023 Hard
- The incorrect rule regarding the determination of significant figures isTS EAMCET 2024 Easy
- For a chemical reaction, the standard Gibbs energy change, \(\Delta G^{\circ}\) is \(-7.64 \times 10^4 \mathrm{~J} \mathrm{~mol}^1\). What is the value of equilibrium constant (K)?TS EAMCET 2019 Medium
- \(1+\cos x+\cos ^2 x+\cos ^3 x+\ldots\) to \(\infty=4+2 \sqrt{3}\), then \(x=\)TS EAMCET 2025 Medium
- The equation of the straight line perpendicular to the straight line \(3 x+2 y=0\) and passing through the point of intersection of the lines \(x+3 y-1=0\) and \(x-2 y+4=0\) isTS EAMCET 2009 Easy