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.