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NCERT Questions for Class 12 Maths Chapter 2 – Inverse Trigonometric Functions

Class 12 Maths Inverse Trigonometric Functions Important questions will help students in getting ready for and to perform well on the CBSE Class 12 Maths exam. These questions are prepared by experts based on the most recent syllabus. It is advised that students should prepare for the board exams by practicing the important questions for every chapter in Class 12 course provided by StudyMaterialsOnline.

Some of the major mathematical functions are those to do with trigonometry, particularly inverse trigonometric functions. These give or tell one the angle when the trigonometric ratio is provided or known. Major important inverse trigonometric functions that a student encounters during class 12 are sin inverse and cos inverse, and tan inverse. These are some of the most important functions, which one must understand to solve any problem related to trigonometry.

Important Questions with Solutions of Class 12 Maths Chapter 2 – Inverse Trigonometric Functions

1) Show that

Ans – Applying the identities of trigonometry

2) Show that

Ans – App¹lying the identities of trigonometry

By removing a common from (1)’s denominator and canceling it out with the numerator, we obtain

Using the trigonometric identity √(1-sin^2 θ) = cos⁡x in the deniminator of (2) we get,

Using the trigonometric identity sin²θ + cos²θ = 1 we get,

3) Show that

When we substitute these values from equations (4) and (8), we obtain,

Hence Proved.

4) Prove that

Ans – To solve this problem substitute,

5) Prove that

Ans – In LHS apply the trigonometric identity,

6) Show that

Ans – On the LHS of the expression apply the trigonometric identity,

7) Evaluate

Ans – In the expression use the substitution

8) Prove that

Ans – On the LHS of the expression apply the trigonometric identity,

9) Find the value of x in the expression 2tan^-1(cos x ) = tan^-1(2cosec x)

Ans – On the LHS of the expression apply the trigonometric identity,

By applying the trigonometric identity sin²x = 1 – cos²x in the denominator of (1) we get,

When the value from equation (2) is substituted into the given expression we obtain,

Key Points to Remember

Inverse Trigonometric Functions have restricted domains in order to exist.
The range is restricted to certain intervals for inverse trigonometric functions.
Inverse trigonometric functions are useful for solving equations having trigonometric functions.
Principal value branches have to be kept in mind when working with inverse trigonometric functions.
The graphs of inverse trigonometric functions possess unique character.

Real-World Application of Inverse Trigonometric Functions

Inverse Trigonometric Functions are used in many areas of sciences like engineering, physics and computer science. They are useful in tackling problems of oscillatory motion, signal processing and navigation systems. So, knowledge of these functions is vital to solve a real world problem that deals with trigonometry.