Prove the following identities (1-16) :

Question 1:

Answer:

LHS

RHS. Hence proved.

Question 2:

Answer:

LHS

RHS. Hence proved.

Question 3:

Answer:

LHS

RHS. 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. Hence proved.

Question 8:

Answer:

LHS

RHS. Hence proved.

Question 9:

Answer:

RHS

= LHS. Hence proved.

Question 10:

Answer:

LHS

RHS. Hence Proved.

Question 11:

Answer:

LHS

RHS. Hence Proved.

Question 12:

Answer:

LHS

RHS. Hence Proved.

Question 13:

Answer:

LHS

RHS. Hence Proved.

Question 14:

Answer:

LHS

Question 15:

Answer:

LHS

RHS. Hence proved.

Question 16:

Answer:

LHS

RHS

Question 17: If , then prove that is also equal to

Answer:

RHS

RHS. Hence proved.

Question 18: If , find the values of and .

Answer:

Given:

Question 19: If , then find the value of

Answer:

Given

Question 20: If , show that

Answer:

LHS

RHS. Hence proved.

Question 21: If , then prove that .

Answer:

Given

Similarly given

Therefore

RHS.

Question 22: If and , then prove that .

Answer:

Given

Also

LHS

RHS

Therefore LHS RHS. Hence proved.

Question 23: If , then prove that , where .

Answer:

Given

RHS

LHS

Therefore LHS RHS. Hence proved.

Question 24: If and , then show that

Answer:

Given:

LHS

RHS. Hence proved.

Question 25: Prove that: , where .

Answer:

LHS

since .

Question 26: If , prove that i) ii)

Answer:

Given

i) LHS

RHS

Therefore LHS RHS. Hence proved.

ii) LHS

. Hence proved.