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# NCERT Solutions class-11 Maths Exercise 3.3

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Exercise 3.3

Prove that:

1.

Ans. 1. L.H.S. =

=

= R.H.S.

2.

Ans. L.H.S. =

=

=

=

=

3.

Ans. L.H.S. =

=

=

=

= = R.H.S.

4.

Ans. L.H.S. =

=

=

=

= = R.H.S.

5. Find the value of:

(i)

(ii)

Ans. (i)

=

(ii)

=

=

Prove the following:

6.

Ans. L.H.S. =

=

= = R.H.S.

7.

Ans. L.H.S. =

[Using ]

= =

= = R.H.S.

8.

Ans. L.H.S. =

= = = R.H.S.

9.

Ans. L.H.S. =

=

=

=

= 1 = R.H.S.

10.

Ans. L.H.S. =

=

=

= = R.H.S.

11.

Ans. L.H.S. =

= =

= =

= = R.H.S.

12.

Ans. L.H.S. =

=

= = R.H.S.

13.

Ans. L.H.S. =

=

= = R.H.S.

14.

Ans. L.H.S. =

=

=

=

=

=

=

= = R.H.S.

15.

Ans. L.H.S. =

=

= =

R.H.S. =

=

= =

L.H.S. = R.H.S.

16.

Ans. L.H.S. =

=

= = R.H.S.

17.

Ans. L.H.S. =

=

= = R.H.S.

18.

Ans. L.H.S. =

=

= = R.H.S.

19.

Ans. L.H.S. =

=

= = R.H.S.

20.

Ans. L.H.S. =

=

=

= = R.H.S.

21.

Ans. L.H.S. =

=

=

=

= = = R.H.S.

22.

Ans. We know that

23.

Ans. L.H.S. =

=

=

=

= = R.H.S.

24.

Ans. L.H.S. =

=

=

= = R.H.S.

25.

Ans. L.H.S. =

=

=

=

= = R.H.S.

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