Question 1: **[2003]**

Answer:

LHS

RHS. Hence proved.

Question 2:

Answer:

LHS

Question 3:

Answer:

RHS

LHS. Hence proved.

Question 4:

Answer:

LHS =

= RHS. Hence proved.

Question 5:

Answer:

LHS

RHS. Hence proved.

Question 6:

Answer:

LHS

RHS. Hence proved.

Question 7:

Answer:

LHS

RHS

Therefore LHS = RHS. Hence proved.

Question 8:

Answer:

LHS

RHS. Hence proved.

Question 9:

Answer:

LHS

Question 10: If and , then prove that

Answer:

Given: and

Squaring both sides we get:

… … … (i)

… … … (ii)

Adding (i) and (ii), we get

. Hence proved.

Question 11: If and , then prove that

Answer:

Given: and

Squaring both sides:

… … … (i)

… … … (ii)

Subtracting (ii) from (i) we get

Hence proved.

Question 12: If , and , then prove that

Answer:

Given: , and

Squaring all and adding, we get:

Hence proved.

Question 13: If and , show that

Answer:

Given: and

Therefore

Hence proved.

Question 14: If , and , show that

Answer:

Given: , and

Squaring all the three equations and adding, we get

Hence proved.

Question 15: If and , show that

Answer:

Given:

Hence proved.