# NCERT Class 11-Math's: Exemplar Chapter 3 Trigonometric Functions Part 6

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**Question 13:**

If angle is divided into two parts such that the tangent of one part is times the tangent of other, and φ is their difference, then show that

**Answer:**

Or

Applying componendo and dividendo, we have

Or

Given that . Therefore,

**Question 14:**

Solve

**Answer:**

Divide the given equation by 2 to get

Thus, the solution are given by, i.e.,

Hence, the solution are

## Objective Type Questions

### Choose the Correct Answer from the Given Four Options Against Each of the Examples 15 to 19

**Question 15:**

If tan is (A)

(B)

(C)

(D) None of these

**Answer:**

Correct choice is B. Since is negative, θ lies either in second quadrant or in fourth quadrant. Thus if lies in the second quadrant or , if lies in the fourth quadrant.

**Question 16:**

If and are the roots of the equation, then *a*, *b* and *c* satisfy the relation.

(A)

(B)

(C)

(D)

**Answer:**

The correct choice is (B).

Given that and are the roots of the equation = (Why?)

Using the identity , we have

**Question 17:**

The greatest value of is

(A)

(B)

(C)

(D)

**Answer:**

(D) is the correct choice, since