# EXERCISE 2.2

Prove the following:(Class 12 ncert solution math exercise 2.2)

Question 1: Prove .

Solution: Let

Hence,

Now,

=L H S

Question 2: Prove .

Solution: Let

Hence,

Now,

Question 3: Prove .

Solution: Since we know that

Now,

Question 4:Prove .

Solution: Since we know that

Now,

Question 5: Write the function in the simplest form:

Solution: Let

Hence,

Question 6: Write the function in the simplest form:

Solution: Let

Hence,

Question 7: Write the function in the simplest form:

Solution: Since,

Hence,

Question 8: Write the function in the simplest form:

Solution:

Question 9: Write the function in the simplest form:

Solution: Let

Hence,

Question 10: Write the function in the simplest form:

Solution: Let

Hence,

Question 11: Write the function in the simplest form:

Solution: Let

Hence,

Therefore,

Question 12: Find the value of

Solution: Since

Hence,

Question 13: Find the value of and .

Solution: Let

Hence,

Now, let

Hence,

Therefore,

Question 14: If , find the value of .

Solution: It is given that

Question 15: If , find the value of .

Solution: It is given that

Since

Therefore,

Question 16: Find the value of .

Solution: Since,

Therefore,

Question 17: Find the value of .

Solution:

Question 18: Find the value of .

Solution: Let

Then,

Therefore,

Now,

Thus, by using (1) and (2)

Question 19: is equal to

(A)

(B)

(C)

(D)

Solution:

Thus, the correct option is B.

Question 20: is equal to

(A)

(B)

(C)

(D) 1

Solution: Let

Hence,

Since, Range of principal value of .

Therefore,

Then,

=1

Thus, the correct option is D.

Question 21: Find the values of is equal to

(A)

(B)

(C) 0

(D)

Solution: Let

Hence,

Therefore,

Now, let

Hence,

Since, Range of principal value of

Therefore,

Then,

Thus, the correct option is B.