
$\cos \left[\cos ^{-1}(-1 / 7)+\sin ^{-1}(-1 / 7)\right]=$
$1)$-1 / 3
2) 0
3)$1 / 3$
4)$4 / 9$
Answer
162k+ views
Hint: First we need to compare the given expression with the general expression to find the value in the place of x. After that, using trigonometric identities we can easily find the solution to the given expression.
Formula Used:
The general equation is $\sin ^{-1}(x)+\cos ^{-1}(x)=\pi / 2$
Complete step by step Solution:
Given that
$\cos \left[\cos ^{-1}(-1 / 7)+\sin ^{-1}(-1 / 7)\right]$
We know that the general equation
$\sin ^{-1}(x)+\cos ^{-1}(x)=\pi / 2$
Here in the place of $\sin ^{-1}(x)+\cos ^{-1}(x)=\pi / 2$ we have $(-1/7)$
So accordingly we can say that the resultant value of the given equation is $\cos \left[\cos ^{-1}(-1 / 7)+\sin ^{-1}(-1 / 7)\right]=\cos \pi / 2$
Thus,
$\cos \left[\cos ^{-1}(-1 / 7)+\sin ^{-1}(-1 / 7)\right]=\cos \pi / 2$
$=0$
Finding the coordinates of the equivalent point (0, 1) on the unit circle and creating an angle of $\pi /2$ radians with the x-axis will yield the value of $\cos \left[\cos ^{-1}(-1 / 7)+\sin ^{-1}(-1 / 7)\right]=\cos \pi / 2$. The x-coordinate is equivalent to the value of 0. ∴ $\cos \pi /2=0$.
Hence, the correct option is 2.
Additional Information: The domain and range of the functions determine the characteristics of inverse trigonometric functions. A greater comprehension of this idea and the ability to solve difficulties both depend on certain aspects of inverse trigonometric functions. Recall that "Arc Functions" is another name for inverse trigonometric functions. They generate the length of the arc required to arrive at a specific value for a given trigonometric function. The range of values that an inverse function is capable of with its specified domain is referred to as the inverse function's range. The collection of all potential independent variables where a function exists is referred to as the function's domain. There is a specific range in which inverse trigonometric functions are defined.
Note: Students should keep in mind all the formulas related to inverse trigonometric functions for solving such types of questions.
Formula Used:
The general equation is $\sin ^{-1}(x)+\cos ^{-1}(x)=\pi / 2$
Complete step by step Solution:
Given that
$\cos \left[\cos ^{-1}(-1 / 7)+\sin ^{-1}(-1 / 7)\right]$
We know that the general equation
$\sin ^{-1}(x)+\cos ^{-1}(x)=\pi / 2$
Here in the place of $\sin ^{-1}(x)+\cos ^{-1}(x)=\pi / 2$ we have $(-1/7)$
So accordingly we can say that the resultant value of the given equation is $\cos \left[\cos ^{-1}(-1 / 7)+\sin ^{-1}(-1 / 7)\right]=\cos \pi / 2$
Thus,
$\cos \left[\cos ^{-1}(-1 / 7)+\sin ^{-1}(-1 / 7)\right]=\cos \pi / 2$
$=0$
Finding the coordinates of the equivalent point (0, 1) on the unit circle and creating an angle of $\pi /2$ radians with the x-axis will yield the value of $\cos \left[\cos ^{-1}(-1 / 7)+\sin ^{-1}(-1 / 7)\right]=\cos \pi / 2$. The x-coordinate is equivalent to the value of 0. ∴ $\cos \pi /2=0$.
Hence, the correct option is 2.
Additional Information: The domain and range of the functions determine the characteristics of inverse trigonometric functions. A greater comprehension of this idea and the ability to solve difficulties both depend on certain aspects of inverse trigonometric functions. Recall that "Arc Functions" is another name for inverse trigonometric functions. They generate the length of the arc required to arrive at a specific value for a given trigonometric function. The range of values that an inverse function is capable of with its specified domain is referred to as the inverse function's range. The collection of all potential independent variables where a function exists is referred to as the function's domain. There is a specific range in which inverse trigonometric functions are defined.
Note: Students should keep in mind all the formulas related to inverse trigonometric functions for solving such types of questions.
Recently Updated Pages
If tan 1y tan 1x + tan 1left frac2x1 x2 right where x frac1sqrt 3 Then the value of y is

Geometry of Complex Numbers – Topics, Reception, Audience and Related Readings

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

JoSAA JEE Main & Advanced 2025 Counselling: Registration Dates, Documents, Fees, Seat Allotment & Cut‑offs

NIT Cutoff Percentile for 2025

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

Degree of Dissociation and Its Formula With Solved Example for JEE

Free Radical Substitution Mechanism of Alkanes for JEE Main 2025

JEE Advanced 2025 Notes
