Exercise 4.5: Inverse Trigonometric Functions

EXERCISE 4.5

1. Find the value, if it exists. If not, give the reason for non-existence.

2. Find the value of the expression in terms of x , with the help of a reference triangle.

3. Find the value of

4.Prove that

5.Prove that tan−1 x + tan−1 y + tan−1 z = tan−1 

6. If  tan−1  x + tan−1  y + tan−1  z = π , show that x + y + z = xyz .

7. Prove that 

8.Simplify 

9. Solve:

10. Find the number of solution of the equation tan-1 ( x -1) + tan-1 x + tan-1 ( x +1) = tan-1 (3x).

Answers: