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**Miscellaneous Exercise**

**Prove that:**

**1. **

**Ans. **L.H.S. =

=

=

=

= = 0 = R.H.S.

**2. **

**Ans. **L.H.S. =

=

=

= = 0 = R.H.S.

**3. **

**Ans. **L.H.S. =

=

=

=

= = R.H.S.

**4. **

**Ans. **L.H.S. =

=

=

=

= = R.H.S.

**5. **

**Ans. **L.H.S. =

=

=

=

=

=

= = R.H.S.

**6. **

**Ans. **L.H.S. =

=

=

=

= = R.H.S.

**7. **

**Ans. **L.H.S. = =

=

=

=

=

=

= = R.H.S.

**Find and in each of the following:**

**8. **** in quadrant II.**

**Ans. **Given: in quadrant II.

=

=

[ lies in II quadrant]

Also

lies in first quadrant.

are positive.

Now,

**9. **** in quadrant III.**

**Ans. **Given: in quadrant III.

Now,

lies in second quadrant.

are positive and are negative.

Now,

**10. **** in quadrant II.**

**Ans. **Given: in quadrant II.

=

=

[ lies in II quadrant]

Also

lies in first quadrant.

are positive.

Now,