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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.

Good morning my friend is coming to get the chance that you can see it

I just love it

realy amazing

It is short mathot… Try it nd by heart

Help full

Question no. 15 have many mistakes. Please check it. I hope you will find it.

exilent

Really helpful.

Problem no 15 has many mistake

So cool

Thank uh for your support….it’s really easy and short methods given hereĀ”!!!!

Thnq fr yur wonderful supprt