# Chapter 3:Miscellaneous Exercise

Prove that(Class 11 Chapter 3 Miscellaneous Exercise trigonometry )

Question 1:

Solution: Given,

Using formula

Question 2:

Solution: Taking

Using formula: and

Question 3:

Solution: Taking

Using formula: and

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Question 4:

Solution: Taking

Using formulae: and

)

Question 5:

Solution: Taking

Using formulae:

Again using formula:

Question 6:

Solution: Taking

Using formula: and

Question 7:

Solution: Taking

Using formula: and

Again using formula:

Find and in each of the following :

Question 8:  if lies in 2nd quadrant.

Solution:  Here, x is in 2nd quadrant.

Therefore ,

Therefore, and are positive.

Given that

We know that

Since,

From the formula:

From formula:

Since,

Hence the value of and are

Question 9: , x in quadrant III

Solution: –Here, x is in IIIrd quadrant.

Therefore ,

Since,

From the formula:

From formula:

Since,

Hence the value of and are

Question 10: , x in quadrant II

Solution: Here, x is in IInd quadrant.

Therefore ,

Formula :

From the formula:

From formula: