Select Goal &
City
Select Goal
Explore
Question:
If \(a=sin^{-1}(sin\ 5)\) and \(b=cos^{-1}(cos\ 5)\), then \(a^2+b^2=\)
If \(a=sin^{-1}(sin\ 5)\) and \(b=cos^{-1}(cos\ 5)\), then \(a^2+b^2=\)
Updated On: Oct 22, 2024
Hide Solution
Verified By Collegedunia
Solution and Explanation
The answer is \(8\pi^2-40\pi+50\).
Was this answer helpful?
8
18
Top Questions on Inverse Trigonometric Functions
- Let the inverse trigonometric functions take principal values. The number of real solutions of the equation \[ 2 \sin^{-1} x + 3 \cos^{-1} x = \frac{2\pi}{5}, \] is ______ .
- JEE Main - 2024
- Mathematics
- Inverse Trigonometric Functions
- If the domain of the function \[\sin^{-1} \left( \frac{3x - 22}{2x - 19} \right) + \log_e \left( \frac{3x^2 - 8x + 5}{x^2 - 3x - 10} \right)\] is \( (\alpha, \beta] \), then \( 3\alpha + 10\beta \) is equal to:
- JEE Main - 2024
- Mathematics
- Inverse Trigonometric Functions
- Considering only the principal values of inverse trigonometric functions, the number of positive real values of \( x \) satisfying \[ \tan^{-1}(x) + \tan^{-1}(2x) = \frac{\pi}{4} \] is:
- JEE Main - 2024
- Mathematics
- Inverse Trigonometric Functions
- Considering only the principal values of the inverse trigonometric functions, the value of
\(\tan(\sin^{-1}(\frac{3}{5})-2\cos^{-1}(\frac{2}{\sqrt5}))\)
is- JEE Advanced - 2024
- Mathematics
- Inverse Trigonometric Functions
- If the sum of all the solutions of $\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)+\cot ^{-1}\left(\frac{1-x^2}{2 x}\right)=\frac{\pi}{3},-1 < x < 1, x \neq 0$, is $\alpha-\frac{4}{\sqrt{3}}$, then $\alpha$ is equal to ___
- JEE Main - 2023
- Mathematics
- Inverse Trigonometric Functions
View More Questions
Questions Asked in JEE Main exam
- The area of the region enclosed by the parabolas \( y = x^2 - 5x \) and \( y = 7x - x^2 \) is _________.
- JEE Main - 2024
- Calculus
- The heat of combustion of solid benzoic acid at constant volume is \(-321.30 \, \text{kJ}\) at \(27^\circ \text{C}\). The heat of combustion at constant pressure is \((-321.30 - xR)\, \text{kJ}\). The value of \(x\) is:
- JEE Main - 2024
- Thermodynamics
- Consider the given chemical reaction sequence :
- JEE Main - 2024
- Aldehydes, Ketones and Carboxylic Acids
[Given atomic number of Cu = 29, Ni = 28,Mn = 25, Fe = 26]- JEE Main - 2024
- Qualitative Analysis
- \(C_{11}H_{18}O_{12}\)The value of the Rydberg constant (\(R_H\)) is \(2.18 \times 10^{-18} \, \text{J}\). The velocity of an electron having mass \(9.1 \times 10^{-31} \, \text{kg}\) in Bohr's first orbit of the hydrogen atom is:\(\dots \times 10^5 \, \text{ms}^{-1}\) (nearest integer).
- JEE Main - 2024
- Atomic Structure
View More Questions
Concepts Used:
Inverse Trigonometric Functions
The inverse trigonometric functions are also called arcus functions or anti trigonometric functions. These are the inverse functions of the trigonometric functions with suitably restricted domains. Specifically, they are the inverse functions of the sine, cosine, tangent, cotangent, secant, and cosecant functions, and are used to obtain an angle from any of the angle’s trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.
Domain and Range Of Inverse Functions
Considering the domain and range of the inverse functions, following formulas are important to be noted:
- sin(sin−1x) = x, if -1 ≤ x ≤ 1
- cos(cos−1x) = x, if -1 ≤ x ≤ 1
- tan(tan−1x) = x, if -∞ ≤ x ≤∞
- cot(cot−1x) = x, if -∞≤ x ≤∞
- sec(sec−1x) = x, if -∞ ≤ x ≤ -1 or 1 ≤ x ≤ ∞
- cosec(cosec−1x) = x, if -∞ ≤ x ≤ -1 or 1 ≤ x ≤ ∞
Also, the following formulas are defined for inverse trigonometric functions.
- sin−1(sin y) = y, if -π/2 ≤ y ≤ π/2
- cos−1(cos y) =y, if 0 ≤ y ≤ π
- tan−1(tan y) = y, if -π/2 <y< π/2
- cot−1(cot y) = y if 0<y< π
- sec−1(sec y) = y, if 0 ≤ y ≤ π, y ≠ π/2
cosec−1(cosec y) = y if -π/2 ≤ y ≤ π/2, y ≠ 0
SUBSCRIBE TO OUR NEWS LETTER
COLLEGE NOTIFICATIONSEXAM NOTIFICATIONSNEWS UPDATES
Download the Collegedunia app on 
© 2024 Collegedunia Web Pvt. Ltd. All Rights Reserved